Exploring the Near-Optimal Feasible Space¶
Here, we use modelling to generate alternatives (MGA) to explore the near-opimal feasible space of a simple one-node model in the style of model.energy (the same as in the previous MGA example).
While we explored the use of n.optimize.optimize_mga() in the previous example, PyPSA includes a few additional functions making it convenient to work with near-optimal spaces in a geometric way. While the optimize_mga function solves a network with an alternative objective function (given by the weights argument), n.optimize_mga_in_direction is a simple alternative useful for exploring trade-offs between multiple alternative objectives. It takes two key arguments: a dictionary of dimensions, specifying multiple alternative objectives in the same format as the previously mentioned weights, and a direction representing a vector in the coordinate space defined by dimensions.
In this example, we explore the trade-offs between wind and solar expansion in a simple renewables-based system. Therefore, we define our dimensions (or alternative objectives) as total installed wind capacity and total installed solar capacity in MW, respectively. These dimensions can also be seen as defining a projection of near-optimal space of the model down to two dimensions.
:::{note} See also this research article for a background on dimension reduction and approximation of near-optimal spaces. :::
In [2]:
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import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from scipy.spatial import ConvexHull, convex_hull_plot_2d
import pypsa
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from scipy.spatial import ConvexHull, convex_hull_plot_2d
import pypsa
Before any near-optimal analysis can start, the model has to be solved to optimality first. This is in order to find the minimum system cost, which is later used to define a system cost bound for near-optimality (i.e. "slack", usually in percentage of minimum system cost).
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n = pypsa.examples.model_energy()
n.snapshots = n.snapshots[::3] # Crude reduction of time resolution for speed
n.generators.at["load shedding", "marginal_cost"] = 20000
n.optimize(solver_name="gurobi")
n = pypsa.examples.model_energy()
n.snapshots = n.snapshots[::3] # Crude reduction of time resolution for speed
n.generators.at["load shedding", "marginal_cost"] = 20000
n.optimize(solver_name="gurobi")
INFO:pypsa.network.io:Imported network 'Model-Energy' has buses, carriers, generators, links, loads, storage_units, stores
/tmp/ipykernel_5356/2365194803.py:4: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. n.optimize(solver_name="gurobi")
INFO:linopy.model: Solve problem using Gurobi solver
INFO:linopy.model:Solver options: - log_to_console: False
INFO:linopy.io: Writing time: 0.12s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-7oz3kxa2.lp
Reading time = 0.02 seconds
obj: 21434 rows, 9746 columns, 41420 nonzeros
Set parameter LogToConsole to value 0
Warning: environment still referenced so free is deferred (Continue to use WLS)
INFO:linopy.constants: Optimization successful: Status: ok Termination condition: optimal Solution: 9746 primals, 21434 duals Objective: 6.90e+09 Solver model: available Solver message: 2
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Generator-ext-p-lower, Generator-ext-p-upper, Link-ext-p-lower, Link-ext-p-upper, Store-ext-e-lower, Store-ext-e-upper, StorageUnit-ext-p_dispatch-lower, StorageUnit-ext-p_dispatch-upper, StorageUnit-ext-p_store-lower, StorageUnit-ext-p_store-upper, StorageUnit-ext-state_of_charge-lower, StorageUnit-ext-state_of_charge-upper, StorageUnit-energy_balance, Store-energy_balance were not assigned to the network.
Out[3]:
('ok', 'optimal')
Individual dimensions are specified just like the weights argument for the n.optimize.optimize_mga function: a nested dictionary of components, variables and finally a series or dictionary giving weights to individual components.
Here, we define two dimensions, and give them the user-defined names "wind" and "solar" (the keys in the outer dictionary). These names are arbitrary and don't have to match names of underlaying components.
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dimensions = {
"wind": {"Generator": {"p_nom": {"wind": 1}}},
"solar": {"Generator": {"p_nom": {"solar": 1}}},
}
dimensions = {
"wind": {"Generator": {"p_nom": {"wind": 1}}},
"solar": {"Generator": {"p_nom": {"solar": 1}}},
}
Suppose we are interested in minimizing wind capacity alone, and also interested in minimizing the total capacity of wind and solar. These correspond to the directions (-1, 0) and (-1, -1) in wind-solar coordinate space, respectively. Let's see what is possible within a 5% total system cost slack.
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_, _, min_wind = n.optimize.optimize_mga_in_direction(
dimensions=dimensions,
direction={
"wind": -1,
"solar": 0,
}, # Use coordinate names matching those given in `dimensions`
slack=0.05,
)
_, _, min_wind_solar = n.optimize.optimize_mga_in_direction(
dimensions=dimensions,
direction={"wind": -1, "solar": -1},
slack=0.05,
)
display(min_wind)
display(min_wind_solar)
_, _, min_wind = n.optimize.optimize_mga_in_direction(
dimensions=dimensions,
direction={
"wind": -1,
"solar": 0,
}, # Use coordinate names matching those given in `dimensions`
slack=0.05,
)
_, _, min_wind_solar = n.optimize.optimize_mga_in_direction(
dimensions=dimensions,
direction={"wind": -1, "solar": -1},
slack=0.05,
)
display(min_wind)
display(min_wind_solar)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.model:Solver options: - log_to_console: False
INFO:linopy.io: Writing time: 0.11s
INFO:linopy.constants: Optimization successful: Status: ok Termination condition: optimal Solution: 9746 primals, 21435 duals Objective: 1.70e+04 Solver model: available Solver message: Optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Generator-ext-p-lower, Generator-ext-p-upper, Link-ext-p-lower, Link-ext-p-upper, Store-ext-e-lower, Store-ext-e-upper, StorageUnit-ext-p_dispatch-lower, StorageUnit-ext-p_dispatch-upper, StorageUnit-ext-p_store-lower, StorageUnit-ext-p_store-upper, StorageUnit-ext-state_of_charge-lower, StorageUnit-ext-state_of_charge-upper, StorageUnit-energy_balance, Store-energy_balance, budget were not assigned to the network.
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.model:Solver options: - log_to_console: False
INFO:linopy.io: Writing time: 0.11s
INFO:linopy.constants: Optimization successful: Status: ok Termination condition: optimal Solution: 9746 primals, 21435 duals Objective: 4.75e+04 Solver model: available Solver message: Optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Generator-ext-p-lower, Generator-ext-p-upper, Link-ext-p-lower, Link-ext-p-upper, Store-ext-e-lower, Store-ext-e-upper, StorageUnit-ext-p_dispatch-lower, StorageUnit-ext-p_dispatch-upper, StorageUnit-ext-p_store-lower, StorageUnit-ext-p_store-upper, StorageUnit-ext-state_of_charge-lower, StorageUnit-ext-state_of_charge-upper, StorageUnit-energy_balance, Store-energy_balance, budget were not assigned to the network.
wind 17006.298742 solar 44921.817858 dtype: float64
wind 29563.944662 solar 17925.539753 dtype: float64
Results are returned as dictionaries represting coordinates in the wind-solar space. The dictionaries use the same user-given coordinate names that we passed in the dimensions argument. We see that minimizing wind alone leads to a large installation of solar, while minimizing both jointly leads to a more balanced solution.
In order to get a full picture of the near-optimal space (projected to the wind and solar dimensions), it is useful to optimize in many directions and consider the convex hull of the resulting points.
Of course, you can use optimize_mga_in_direction manually to do this. For convenience, PyPSA also provides the optimize_mga_in_multiple_directions function. This function takes a list of directions (or a pandas DataFrame with rows for directions), and uses built-in Python multiprocessing functionality to optimize in these directions in parallel. In the event of any individual optimisations failing, only the successful ones are returned.
While the user is free to select directions themselves, PyPSA also includes some simple functions (for instance, pypsa.optimization.mga.generate_directions_randomber of random directions in the format expected by optimize_mga_in_multiple_directions`.
In [6]:
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directions = pypsa.optimization.mga.generate_directions_random(
dimensions.keys(), 10, seed=0
)
dirs, pts = n.optimize.optimize_mga_in_multiple_directions(
dimensions=dimensions,
directions=directions,
slack=0.05,
solver_name="gurobi",
# Solve in up to 8 directions in parallel.
max_parallel=8,
)
directions = pypsa.optimization.mga.generate_directions_random(
dimensions.keys(), 10, seed=0
)
dirs, pts = n.optimize.optimize_mga_in_multiple_directions(
dimensions=dimensions,
directions=directions,
slack=0.05,
solver_name="gurobi",
# Solve in up to 8 directions in parallel.
max_parallel=8,
)
INFO:pypsa.network.io:Exported network 'Model-Energy' saved to '/tmp/tmptykhzhwr.nc contains: links, sub_networks, storage_units, stores, generators, carriers, loads, buses
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-ctgq24mi.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xf6adfdd5
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-b067iw91.lp
Reading time = 0.09 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Presolve removed 11188 rows and 1442 columns
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x66aa13ad
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-8no4gccm.lp
Reading time = 0.12 seconds
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5379766e+05 7.368053e+06 0.000000e+00 0s
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x2617db0e
Model has 2 linear objective coefficients
Set parameter WLSAccessID
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Set parameter WLSSecret
Objective range [4e-01, 9e-01]
Set parameter LicenseID to value 2537914
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.08s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.3639880e+04 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-j4w57833.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd070ee74
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3442995e+05 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Read LP format model from file /tmp/linopy-problem-xcxrxmie.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x9fcccd7c
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 7e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.6928244e+05 9.633758e+06 0.000000e+00 0s
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-7354ur9s.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x04effe46
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-1zlmf5nl.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x64caf6e1
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3798615e+05 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Read LP format model from file /tmp/linopy-problem-nuh0ba3d.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Model fingerprint: 0x67db4be0
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.6620443e+05 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.6298652e+04 7.368053e+06 0.000000e+00 0s
5635 -5.2066596e+04 0.000000e+00 0.000000e+00 2s Solved in 5635 iterations and 2.13 seconds (0.69 work units) Optimal objective -5.206659614e+04
5672 -5.1731219e+04 0.000000e+00 0.000000e+00 2s Solved in 5672 iterations and 2.44 seconds (0.77 work units) Optimal objective -5.173121946e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
6471 -6.6926816e+04 0.000000e+00 0.000000e+00 4s
Solved in 6471 iterations and 3.55 seconds (1.20 work units)
Optimal objective -6.692681594e+04
5771 -4.6561264e+04 0.000000e+00 0.000000e+00 3s
Solved in 5771 iterations and 2.77 seconds (0.85 work units)
Optimal objective -4.656126351e+04
6443 -7.2295098e+04 0.000000e+00 0.000000e+00 4s Solved in 6443 iterations and 3.56 seconds (1.19 work units) Optimal objective -7.229509830e+04
6152 -7.2077107e+04 0.000000e+00 0.000000e+00 3s
Solved in 6152 iterations and 3.48 seconds (1.16 work units)
Optimal objective -7.207710721e+04
6470 -5.5064409e+04 0.000000e+00 0.000000e+00 4s
Solved in 6470 iterations and 3.81 seconds (1.26 work units)
Optimal objective -5.506440906e+04
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
7148 2.8475167e+04 7.612730e+09 0.000000e+00 5s
8722 3.3049430e+04 0.000000e+00 0.000000e+00 8s Solved in 8722 iterations and 8.06 seconds (2.43 work units) Optimal objective 3.304943025e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-3lgxfyre.lp
Reading time = 0.05 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd7e02e73
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.03s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7175894e+05 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-60n_cx5k.lp
Reading time = 0.04 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x15199912
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.03s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.8730629e+04 7.368053e+06 0.000000e+00 0s
6880 -6.6602029e+04 0.000000e+00 0.000000e+00 1s Solved in 6880 iterations and 0.85 seconds (1.19 work units) Optimal objective -6.660202891e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
7048 -2.7732366e+04 0.000000e+00 0.000000e+00 1s Solved in 7048 iterations and 1.05 seconds (1.52 work units) Optimal objective -2.773236587e+04 Warning: environment still referenced so free is deferred (Continue to use WLS)
The results are returned in the form of two pandas DataFrames; one for directions and one for resulting points / coordinates. Using scipy, we can compute and plot the convex hull of the points we generated.
In [7]:
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display(pts.head() / 1e3)
fig, ax = plt.subplots(figsize=(8, 6))
convex_hull_plot_2d(ConvexHull(pts / 1e3), ax)
ax.axis("equal")
ax.set_xlabel("Wind capacity (GW)")
ax.set_ylabel("Solar capacity (GW)")
ax.set_title("Near-optimal space in wind-solar coordinate space")
plt.show()
display(pts.head() / 1e3)
fig, ax = plt.subplots(figsize=(8, 6))
convex_hull_plot_2d(ConvexHull(pts / 1e3), ax)
ax.axis("equal")
ax.set_xlabel("Wind capacity (GW)")
ax.set_ylabel("Solar capacity (GW)")
ax.set_title("Near-optimal space in wind-solar coordinate space")
plt.show()
| wind | solar | |
|---|---|---|
| 0 | 17.037387 | 70.267029 |
| 1 | 49.546872 | 16.643482 |
| 2 | 15.133119 | 70.067082 |
| 3 | 15.910653 | 70.305473 |
| 4 | 50.504400 | 9.922783 |
While random directions generally work well, they are not always perfectly spaced out. In two dimensions, we can easily generate evenly spaced directions (points on a circle); implemented in PyPSA in pypsa.optimization.mga.generate_directions_evenly_spaced. In higher dimensions, generating evenly spaced directions is not trivial, but Halton sequences (pypsa.optimization.mga.generate_directions_halton) do a better job than randomly generated directions.
In [8]:
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n_points = 20
directions_random = pypsa.optimization.mga.generate_directions_random(
dimensions.keys(), n_points, seed=0
)
directions_even = pypsa.optimization.mga.generate_directions_evenly_spaced(
dimensions.keys(), n_points
)
directions_halton = pypsa.optimization.mga.generate_directions_halton(
dimensions.keys(), n_points, seed=0
)
fig, axs = plt.subplots(1, 3, figsize=(12, 3), sharey=True)
directions_random.plot(kind="scatter", x="wind", y="solar", ax=axs[0])
directions_even.plot(kind="scatter", x="wind", y="solar", ax=axs[1])
directions_halton.plot(kind="scatter", x="wind", y="solar", ax=axs[2])
for ax in axs:
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.axis("equal")
plt.show()
n_points = 20
directions_random = pypsa.optimization.mga.generate_directions_random(
dimensions.keys(), n_points, seed=0
)
directions_even = pypsa.optimization.mga.generate_directions_evenly_spaced(
dimensions.keys(), n_points
)
directions_halton = pypsa.optimization.mga.generate_directions_halton(
dimensions.keys(), n_points, seed=0
)
fig, axs = plt.subplots(1, 3, figsize=(12, 3), sharey=True)
directions_random.plot(kind="scatter", x="wind", y="solar", ax=axs[0])
directions_even.plot(kind="scatter", x="wind", y="solar", ax=axs[1])
directions_halton.plot(kind="scatter", x="wind", y="solar", ax=axs[2])
for ax in axs:
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.axis("equal")
plt.show()
In [9]:
Copied!
fig, axs = plt.subplots(1, 3, figsize=(12, 3), sharey=True)
for ax, directions in zip(axs, [directions_random, directions_even, directions_halton]):
_, pts = n.optimize.optimize_mga_in_multiple_directions(
dimensions=dimensions,
directions=directions,
slack=0.05,
solver_name="gurobi",
max_parallel=8,
)
convex_hull_plot_2d(ConvexHull(pts / 1e3), ax)
ax.axis("equal")
ax.set_xlabel("Wind capacity (GW)")
ax.set_ylabel("Solar capacity (GW)")
plt.show()
fig, axs = plt.subplots(1, 3, figsize=(12, 3), sharey=True)
for ax, directions in zip(axs, [directions_random, directions_even, directions_halton]):
_, pts = n.optimize.optimize_mga_in_multiple_directions(
dimensions=dimensions,
directions=directions,
slack=0.05,
solver_name="gurobi",
max_parallel=8,
)
convex_hull_plot_2d(ConvexHull(pts / 1e3), ax)
ax.axis("equal")
ax.set_xlabel("Wind capacity (GW)")
ax.set_ylabel("Solar capacity (GW)")
plt.show()
INFO:pypsa.network.io:Exported network 'Model-Energy' saved to '/tmp/tmp98babmz0.nc contains: links, sub_networks, storage_units, stores, generators, carriers, loads, buses
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-x2qtuqg6.lp
Reading time = 0.09 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xf6adfdd5
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-98159vie.lp
Reading time = 0.10 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd070ee74
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.08s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.08s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5379766e+05 7.368053e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.6928244e+05 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-ckx8_3v8.lp
Reading time = 0.15 seconds
Set parameter WLSAccessID
obj: 21435 rows, 9746 columns, 42400 nonzeros
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x2617db0e
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-3i7k3kk3.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x66aa13ad
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-038b5lzt.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x04effe46
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-4u9r5o1t.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x64caf6e1
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-zp2ee12x.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x67db4be0
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3442995e+05 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.3639880e+04 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.6620443e+05 9.633758e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3798615e+05 7.368053e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.6298652e+04 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-d7we1y3j.lp
Reading time = 0.21 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x9fcccd7c
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 7e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
5635 -5.2066596e+04 0.000000e+00 0.000000e+00 2s Solved in 5635 iterations and 2.34 seconds (0.69 work units) Optimal objective -5.206659614e+04
5672 -5.1731219e+04 0.000000e+00 0.000000e+00 3s Solved in 5672 iterations and 2.56 seconds (0.77 work units) Optimal objective -5.173121946e+04
5771 -4.6561264e+04 0.000000e+00 0.000000e+00 3s
Solved in 5771 iterations and 2.71 seconds (0.85 work units)
Optimal objective -4.656126351e+04
6443 -7.2295098e+04 0.000000e+00 0.000000e+00 3s
Solved in 6443 iterations and 3.40 seconds (1.19 work units)
Optimal objective -7.229509830e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6471 -6.6926816e+04 0.000000e+00 0.000000e+00 4s
Solved in 6471 iterations and 3.54 seconds (1.20 work units)
Optimal objective -6.692681594e+04
6152 -7.2077107e+04 0.000000e+00 0.000000e+00 3s Solved in 6152 iterations and 3.35 seconds (1.16 work units) Optimal objective -7.207710721e+04 Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
6470 -5.5064409e+04 0.000000e+00 0.000000e+00 4s
Solved in 6470 iterations and 3.85 seconds (1.26 work units)
Optimal objective -5.506440906e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
7148 2.8475167e+04 7.612730e+09 0.000000e+00 5s
8722 3.3049430e+04 0.000000e+00 0.000000e+00 8s Solved in 8722 iterations and 8.22 seconds (2.43 work units) Optimal objective 3.304943025e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-d3uq3qkc.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x15199912
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.8730629e+04 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-n20kmvxv.lp
Reading time = 0.10 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x9e1ed54d
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-849_66l2.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd7e02e73
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.08s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.4925769e+05 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7175894e+05 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-79h1_nl0.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd3f19c53
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-38xp8kh1.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x9922d852
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-qecozbzo.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd50bbc7c
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -5.3598006e+04 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5428928e+05 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.2148863e+05 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-ols8f_qc.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x2571a97d
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.9512478e+04 7.368053e+06 0.000000e+00 0s
7724 -5.3742312e+04 0.000000e+00 0.000000e+00 3s Solved in 7724 iterations and 3.21 seconds (1.09 work units) Optimal objective -5.374231227e+04
6880 -6.6602029e+04 0.000000e+00 0.000000e+00 3s Solved in 6880 iterations and 3.44 seconds (1.19 work units) Optimal objective -6.660202891e+04
7048 -2.7732366e+04 0.000000e+00 0.000000e+00 4s Solved in 7048 iterations and 4.42 seconds (1.52 work units) Optimal objective -2.773236587e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
6157 -4.8794692e+03 0.000000e+00 0.000000e+00 3s
Solved in 6157 iterations and 3.43 seconds (1.05 work units)
Optimal objective -4.879469197e+03
Warning: environment still referenced so free is deferred (Continue to use WLS)
6341 -4.5234577e+04 0.000000e+00 0.000000e+00 4s
Solved in 6341 iterations and 3.97 seconds (1.24 work units)
Optimal objective -4.523457661e+04
6668 -6.7487441e+04 0.000000e+00 0.000000e+00 4s Solved in 6668 iterations and 4.12 seconds (1.28 work units) Optimal objective -6.748744132e+04
6606 -1.0756655e+04 0.000000e+00 0.000000e+00 5s Solved in 6606 iterations and 4.68 seconds (1.43 work units) Optimal objective -1.075665538e+04 Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de Read LP format model from file /tmp/linopy-problem-f5ut65np.lp Reading time = 0.14 seconds obj: 21435 rows, 9746 columns, 42400 nonzeros Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS") CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2] Thread count: 1 physical cores, 2 logical processors, using up to 2 threads Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min) Model fingerprint: 0x41451f27
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Warning: environment still referenced so free is deferred (Continue to use WLS)
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.1816197e+05 7.368053e+06 0.000000e+00 0s
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
6515 -4.3359725e+04 0.000000e+00 0.000000e+00 4s Solved in 6515 iterations and 3.71 seconds (1.31 work units) Optimal objective -4.335972543e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-vh9utj_t.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x85895608
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.06s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.6982127e+04 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-5bjqwz0c.lp
Reading time = 0.07 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x2600b36d
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.06s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3112767e+05 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-fflelvn3.lp
Reading time = 0.08 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x1f619ad7
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.07s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-owqaz7eq.lp
Reading time = 0.04 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd4f6527b
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 7e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3184565e+05 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.03s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.6686658e+05 9.633758e+06 0.000000e+00 0s
5416 -5.2172614e+04 0.000000e+00 0.000000e+00 1s Solved in 5416 iterations and 1.07 seconds (0.67 work units) Optimal objective -5.217261417e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6523 -3.2980815e+03 0.000000e+00 0.000000e+00 2s
Solved in 6523 iterations and 2.09 seconds (1.40 work units)
Optimal objective -3.298081486e+03
6579 -6.3002162e+04 0.000000e+00 0.000000e+00 2s
Solved in 6579 iterations and 1.56 seconds (1.13 work units)
Optimal objective -6.300216196e+04
6481 -5.0846373e+04 0.000000e+00 0.000000e+00 2s Solved in 6481 iterations and 1.86 seconds (1.27 work units) Optimal objective -5.084637343e+04
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
INFO:pypsa.network.io:Exported network 'Model-Energy' saved to '/tmp/tmpoywh4l5f.nc contains: links, sub_networks, storage_units, stores, generators, carriers, loads, buses
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-cd08kr3f.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x6c2f7eae
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-vhvpav57.lp
Reading time = 0.10 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Read LP format model from file /tmp/linopy-problem-6b5rf57n.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe9a8a415
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Model fingerprint: 0xe2b39f95
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-u8w835mx.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb7123fa5
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
0 -1.4811475e+05 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-z4po2q3w.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xa20fc73d
Model has 1 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-afemtd9p.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe7a9370b
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Read LP format model from file /tmp/linopy-problem-xb4cvb9t.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x78333845
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5518740e+05 9.633758e+06 0.000000e+00 0s
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7223651e+05 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.2294746e+05 9.633758e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.8672572e+04 7.368053e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7242591e+05 9.633758e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.2599393e+05 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-uwx3_m57.lp
Reading time = 0.20 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x2e54a80c
Model has 1 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-17, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5573706e+05 9.633758e+06 0.000000e+00 0s
5821 -5.2432650e+04 0.000000e+00 0.000000e+00 2s Solved in 5821 iterations and 2.24 seconds (0.72 work units) Optimal objective -5.243264984e+04
5707 -5.0724971e+04 0.000000e+00 0.000000e+00 3s
Solved in 5707 iterations and 2.63 seconds (0.82 work units)
Optimal objective -5.072497059e+04
6206 -5.6458286e+04 0.000000e+00 0.000000e+00 3s
Solved in 6206 iterations and 2.85 seconds (0.93 work units)
Optimal objective -5.645828605e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6366 -6.1976214e+04 0.000000e+00 0.000000e+00 4s
Solved in 6366 iterations and 3.66 seconds (1.19 work units)
Optimal objective -6.197621445e+04
6919 -6.7034287e+04 0.000000e+00 0.000000e+00 4s
Solved in 6919 iterations and 3.61 seconds (1.21 work units)
Optimal objective -6.703428750e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6225 -7.2092758e+04 0.000000e+00 0.000000e+00 4s
Solved in 6225 iterations and 3.50 seconds (1.17 work units)
Optimal objective -7.209275780e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6415 -4.7821859e+04 0.000000e+00 0.000000e+00 4s
Solved in 6415 iterations and 3.83 seconds (1.26 work units)
Optimal objective -4.782185931e+04
6182 -7.0326701e+04 0.000000e+00 0.000000e+00 4s
Solved in 6182 iterations and 3.53 seconds (1.18 work units)
Optimal objective -7.032670084e+04
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-tn76knmm.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x749e2359
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.1539950e+04 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-nra3b7e6.lp
Reading time = 0.10 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x8a4accd8
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.07s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Read LP format model from file /tmp/linopy-problem-9s3ws2r6.lp
Reading time = 0.11 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd3732619
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-6yyov6z3.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb6efab73
Model has 1 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e-16, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-i43q2lne.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xc07a0636
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.9072290e-11 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-nqotdwck.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xf6ed7abb
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -4.8125400e+04 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-o19l6yry.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb4f76f4d
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-w0psixhg.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x4a406bd1
Model has 1 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-16, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
6953 -2.9160517e+04 0.000000e+00 0.000000e+00 5s Solved in 6953 iterations and 4.57 seconds (1.50 work units) Optimal objective -2.916051670e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6356 1.1952137e+04 0.000000e+00 0.000000e+00 4s
Solved in 6356 iterations and 4.33 seconds (1.31 work units)
Optimal objective 1.195213724e+04
6630 -8.2668519e+03 0.000000e+00 0.000000e+00 4s Solved in 6630 iterations and 4.41 seconds (1.42 work units) Optimal objective -8.266851916e+03
7724 2.2455899e+04 2.179345e+08 0.000000e+00 5s
7038 3.0310872e+04 2.962853e+08 0.000000e+00 5s
Warning: environment still referenced so free is deferred (Continue to use WLS)
7008 2.3605657e+04 4.047573e+07 0.000000e+00 5s
Warning: environment still referenced so free is deferred (Continue to use WLS)
6938 1.1627412e+04 1.935256e+10 0.000000e+00 5s
6398 6.9748192e+03 0.000000e+00 0.000000e+00 5s
Solved in 6398 iterations and 4.74 seconds (1.41 work units)
Optimal objective 6.974819239e+03
Warning: environment still referenced so free is deferred (Continue to use WLS)
9134 2.7690298e+04 0.000000e+00 0.000000e+00 8s Solved in 9134 iterations and 8.06 seconds (2.34 work units) Optimal objective 2.769029817e+04
8659 3.0218089e+04 0.000000e+00 0.000000e+00 8s
Solved in 8659 iterations and 8.24 seconds (2.42 work units)
Optimal objective 3.021808906e+04
8646 3.3561192e+04 0.000000e+00 0.000000e+00 9s
Solved in 8646 iterations and 8.56 seconds (2.47 work units)
Optimal objective 3.356119221e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
9090 2.0404229e+04 0.000000e+00 0.000000e+00 9s Solved in 9090 iterations and 8.77 seconds (2.58 work units) Optimal objective 2.040422855e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de Read LP format model from file /tmp/linopy-problem-ltp4tmgo.lp Reading time = 0.12 seconds obj: 21435 rows, 9746 columns, 42400 nonzeros Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS") CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2] Thread count: 1 physical cores, 2 logical processors, using up to 2 threads Read LP format model from file /tmp/linopy-problem-01iqr89v.lp Reading time = 0.11 seconds obj: 21435 rows, 9746 columns, 42400 nonzeros Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS") CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2] Thread count: 1 physical cores, 2 logical processors, using up to 2 threads Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x52c64967
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-hu1mhfpa.lp
Reading time = 0.06 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x412f885b
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -2.4311162e+04 7.368053e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -6.3647448e+04 7.368053e+06 0.000000e+00 0s
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x25c5fa68
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.23s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -4.6242577e+04 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-ytnrkxg6.lp
Reading time = 0.08 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x62177839
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.06s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.4822062e+04 7.368053e+06 0.000000e+00 0s
6102 -7.9253582e+03 0.000000e+00 0.000000e+00 1s
Solved in 6102 iterations and 1.47 seconds (1.02 work units)
Optimal objective -7.925358241e+03
6022 -3.5221641e+04 0.000000e+00 0.000000e+00 2s
Solved in 6022 iterations and 1.53 seconds (0.97 work units)
Optimal objective -3.522164125e+04
6002 -2.2520548e+04 0.000000e+00 0.000000e+00 2s Solved in 6002 iterations and 1.63 seconds (0.97 work units) Optimal objective -2.252054807e+04 Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
5861 -4.4977783e+04 0.000000e+00 0.000000e+00 1s
Solved in 5861 iterations and 1.32 seconds (0.88 work units)
Optimal objective -4.497778343e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
INFO:pypsa.network.io:Exported network 'Model-Energy' saved to '/tmp/tmp_k_ivsxm.nc contains: links, sub_networks, storage_units, stores, generators, carriers, loads, buses
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-t0_k1ich.lp
Reading time = 0.11 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x0d76bf87
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-kj9xvrr4.lp
Reading time = 0.11 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x0e59cf06
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7430028e+05 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-_wegcz_3.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x4d5b70fd
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [8e-02, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-i75k71mz.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x7352f468
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-vl3cfwyl.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x7f7ca0ae
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 7e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-t0hm7v76.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x170fea55
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-03, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-qxuhqunw.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe482597e
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -5.9464899e+03 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-gf99onlt.lp
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Iteration Objective Primal Inf. Dual Inf. Time
Model fingerprint: 0x47d2e2f3
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
0 -5.6768161e+04 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.8670461e+04 7.368053e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.1973481e+05 7.368053e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.5806004e+04 7.368053e+06 0.000000e+00 0s
5593 -5.0635024e+04 0.000000e+00 0.000000e+00 2s Solved in 5593 iterations and 2.45 seconds (0.77 work units) Optimal objective -5.063502359e+04
6001 -3.0007623e+04 0.000000e+00 0.000000e+00 3s
Solved in 6001 iterations and 3.20 seconds (0.97 work units)
Optimal objective -3.000762303e+04
6734 -7.1107614e+04 0.000000e+00 0.000000e+00 4s
Solved in 6734 iterations and 3.61 seconds (1.24 work units)
Optimal objective -7.110761433e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6177 3.4437487e+03 0.000000e+00 0.000000e+00 3s Solved in 6177 iterations and 3.49 seconds (1.05 work units) Optimal objective 3.443748662e+03
6368 -4.4242681e+04 0.000000e+00 0.000000e+00 4s Solved in 6368 iterations and 3.90 seconds (1.26 work units) Optimal objective -4.424268136e+04 Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
7048 3.0362319e+04 3.544065e+08 0.000000e+00 5s
6579 -2.7810716e+03 0.000000e+00 0.000000e+00 5s
Solved in 6579 iterations and 4.54 seconds (1.44 work units)
Optimal objective -2.781071592e+03
Warning: environment still referenced so free is deferred (Continue to use WLS)
7058 5.0697226e+03 3.573995e+09 0.000000e+00 5s
Warning: environment still referenced so free is deferred (Continue to use WLS)
8651 3.3601172e+04 0.000000e+00 0.000000e+00 8s Solved in 8651 iterations and 8.05 seconds (2.36 work units) Optimal objective 3.360117210e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
9006 1.2176999e+04 0.000000e+00 0.000000e+00 9s
Solved in 9006 iterations and 8.58 seconds (2.54 work units)
Optimal objective 1.217699932e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-hriyh14c.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x6aa20f74
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -6.9725138e+04 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-9p9hgsjw.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x8700c730
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.0155881e+05 7.368053e+06 0.000000e+00 0s
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-fzj2evr8.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x0d8726e8
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-602j5x1x.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xa3e78eb3
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7437996e+05 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-mqk_3207.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd9b6ed2a
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e-01, 7e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-a0x6nvce.lp
Reading time = 0.22 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x4754bf3e
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.6743547e+05 9.633758e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -6.6448961e+04 7.368053e+06 0.000000e+00 0s
5883 -4.0241286e+04 0.000000e+00 0.000000e+00 3s
Solved in 5883 iterations and 2.64 seconds (0.90 work units)
Optimal objective -4.024128564e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6937 -6.9869759e+04 0.000000e+00 0.000000e+00 4s
Solved in 6937 iterations and 3.75 seconds (1.27 work units)
Optimal objective -6.986975898e+04
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
6638 -3.4345283e+04 0.000000e+00 0.000000e+00 4s
Solved in 6638 iterations and 4.30 seconds (1.38 work units)
Optimal objective -3.434528269e+04
Read LP format model from file /tmp/linopy-problem-3119dzfg.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x7b2449af
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e-01, 9e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
5920 -3.7468631e+04 0.000000e+00 0.000000e+00 3s
Solved in 5920 iterations and 2.88 seconds (0.92 work units)
Optimal objective -3.746863085e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
6718 -6.3379285e+04 0.000000e+00 0.000000e+00 3s
Solved in 6718 iterations and 3.27 seconds (1.16 work units)
Optimal objective -6.337928506e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
7937 2.9447106e+04 3.369217e+07 0.000000e+00 5s
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-cj2xvpmq.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x203c7c2a
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5917709e+05 9.633758e+06 0.000000e+00 0s
9032 3.0988504e+04 0.000000e+00 0.000000e+00 7s Solved in 9032 iterations and 7.38 seconds (2.37 work units) Optimal objective 3.098850394e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
7278 1.7386461e+04 2.086869e+07 0.000000e+00 5s
8129 -5.8521164e+04 0.000000e+00 0.000000e+00 4s Solved in 8129 iterations and 3.61 seconds (1.26 work units) Optimal objective -5.852116407e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
8935 2.4156690e+04 0.000000e+00 0.000000e+00 8s Solved in 8935 iterations and 8.09 seconds (2.44 work units) Optimal objective 2.415669002e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-7vfnlh_l.lp
Reading time = 0.09 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x5452b1b9
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.06s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 9.443374e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-cxg8phzl.lp
Reading time = 0.09 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x83c0fa9e
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e-01, 8e-01]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.05s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 -4.2752772e+04 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-70ixf5r0.lp
Reading time = 0.09 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xbf11e364
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.06s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.5390088e+05 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-uj0n6gsc.lp
Reading time = 0.08 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x3fb26852
Model has 2 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [8e-02, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.06s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.0829777e+04 9.633758e+06 0.000000e+00 0s
6047 -2.0107193e+04 0.000000e+00 0.000000e+00 1s Solved in 6047 iterations and 1.46 seconds (1.00 work units) Optimal objective -2.010719254e+04
5789 -5.1573258e+04 0.000000e+00 0.000000e+00 1s
Solved in 5789 iterations and 1.20 seconds (0.80 work units)
Optimal objective -5.157325794e+04
6421 -6.7040531e+04 0.000000e+00 0.000000e+00 2s
Solved in 6421 iterations and 1.70 seconds (1.18 work units)
Optimal objective -6.704053115e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
8867 2.4637395e+04 0.000000e+00 0.000000e+00 4s Solved in 8867 iterations and 3.70 seconds (2.37 work units) Optimal objective 2.463739495e+04
Warning: environment still referenced so free is deferred (Continue to use WLS)
While more difficult to visualize, more than two dimensions can be used to analyse near-optimal spaces. Suppose we are interested in the mutual trade-offs between wind, solar and energy storage. Storage, as a sum of battery and hydrogen storage, is easily defined as a third dimension. In this case, since we are comparing different kinds of components with heterogenous units, it makes sense to scale our dimensions by capital cost in order to get comparable investment numbers.
In [10]:
Copied!
dimensions = {
"wind": {"Generator": {"p_nom": {"wind": n.generators.at["wind", "capital_cost"]}}},
"solar": {
"Generator": {"p_nom": {"solar": n.generators.at["solar", "capital_cost"]}}
},
"storage": {
"StorageUnit": {
"p_nom": {
"battery storage": n.storage_units.at["battery storage", "capital_cost"]
}
},
"Store": {
"e_nom": {
"hydrogen storage": n.stores.at["hydrogen storage", "capital_cost"]
}
},
"Link": {"p_nom": n.links.capital_cost},
},
}
directions = pypsa.optimization.mga.generate_directions_halton(
dimensions.keys(), 50, seed=0
)
dirs, pts = n.optimize.optimize_mga_in_multiple_directions(
dimensions=dimensions,
directions=directions,
slack=0.05,
solver_name="gurobi",
max_parallel=8,
)
dimensions = {
"wind": {"Generator": {"p_nom": {"wind": n.generators.at["wind", "capital_cost"]}}},
"solar": {
"Generator": {"p_nom": {"solar": n.generators.at["solar", "capital_cost"]}}
},
"storage": {
"StorageUnit": {
"p_nom": {
"battery storage": n.storage_units.at["battery storage", "capital_cost"]
}
},
"Store": {
"e_nom": {
"hydrogen storage": n.stores.at["hydrogen storage", "capital_cost"]
}
},
"Link": {"p_nom": n.links.capital_cost},
},
}
directions = pypsa.optimization.mga.generate_directions_halton(
dimensions.keys(), 50, seed=0
)
dirs, pts = n.optimize.optimize_mga_in_multiple_directions(
dimensions=dimensions,
directions=directions,
slack=0.05,
solver_name="gurobi",
max_parallel=8,
)
INFO:pypsa.network.io:Exported network 'Model-Energy' saved to '/tmp/tmpmksqftje.nc contains: links, sub_networks, storage_units, stores, generators, carriers, loads, buses
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-aygv7m0r.lp
Reading time = 0.09 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x97aaca14
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.08s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-c6gorbko.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.7020281e+09 7.368053e+06 0.000000e+00 0s
Model fingerprint: 0x976fd96b
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [9e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-cia2wiie.lp
Reading time = 0.11 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x8143fed2
Read LP format model from file /tmp/linopy-problem-ep9udkfo.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe07df83c
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e-01, 7e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-sh6bxwla.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Model fingerprint: 0xd05aad5a
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [9e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.4743212e+31 4.202370e+28 9.474321e+01 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.0567208e+10 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-dbkov0h8.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe323ba01
Iteration Objective Primal Inf. Dual Inf. Time
0 -2.3795261e+29 4.202370e+28 2.379526e-01 0s
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.6140683e+31 4.202370e+28 8.614068e+01 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Read LP format model from file /tmp/linopy-problem-e95kz9mc.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x6796faed
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e+01, 9e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.0104608e+09 9.633758e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-11jt6e6l.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x4fad4e6f
Presolve removed 11188 rows and 1442 columns
Model has 6 linear objective coefficients
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 7.365790e+06 0.000000e+00 0s
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -6.0046597e+09 7.368053e+06 0.000000e+00 0s
5933 4.3390495e+08 0.000000e+00 0.000000e+00 2s Solved in 5933 iterations and 2.31 seconds (0.71 work units) Optimal objective 4.339049537e+08
6857 -3.3834277e+09 0.000000e+00 0.000000e+00 3s
Solved in 6857 iterations and 2.83 seconds (0.97 work units)
Optimal objective -3.383427665e+09
4992 -3.3604101e+09 0.000000e+00 0.000000e+00 3s
Solved in 4992 iterations and 2.99 seconds (0.97 work units)
Optimal objective -3.360410114e+09
6700 1.1246559e+09 0.000000e+00 0.000000e+00 4s
Solved in 6700 iterations and 3.55 seconds (1.18 work units)
Optimal objective 1.124655890e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
6163 -8.0390419e+08 0.000000e+00 0.000000e+00 3s
Solved in 6163 iterations and 2.91 seconds (0.97 work units)
Optimal objective -8.039041907e+08
6021 -4.9072205e+09 0.000000e+00 0.000000e+00 4s
Solved in 6021 iterations and 3.54 seconds (1.23 work units)
Optimal objective -4.907220499e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
5678 -1.9508534e+09 1.471633e+08 0.000000e+00 5s
8731 1.9864127e+09 5.955793e+08 0.000000e+00 5s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
6985 -1.4109376e+09 0.000000e+00 0.000000e+00 8s Solved in 6985 iterations and 7.76 seconds (2.70 work units) Optimal objective -1.410937604e+09 10343 3.0573976e+09 0.000000e+00 0.000000e+00 8s Solved in 10343 iterations and 7.65 seconds (2.46 work units) Optimal objective 3.057397558e+09
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-5hrl0edq.lp
Reading time = 0.10 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb1867fa0
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3451224e+31 4.202370e+28 1.345122e+01 0s
Read LP format model from file /tmp/linopy-problem-bfyi_ms6.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x5a587057
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -5.4671839e+09 7.368053e+06 0.000000e+00 0s
Read LP format model from file /tmp/linopy-problem-i3lppgc2.lp
Reading time = 0.19 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x5cd654a4
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Set parameter WLSAccessID
Read LP format model from file /tmp/linopy-problem-fju3l8sk.lp
Reading time = 0.19 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb0a5a43e
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e+01, 8e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.4203465e+32 4.202370e+28 1.420346e+02 0s
Read LP format model from file /tmp/linopy-problem-c9ria00j.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xf449290b
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -5.1890004e+31 4.202370e+28 5.189000e+01 0s
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -2.6531247e+31 4.202370e+28 2.653125e+01 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-ecw0b7kw.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xdedc8a05
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 7.365790e+06 0.000000e+00 0s
5478 -2.0722940e+09 0.000000e+00 0.000000e+00 3s Solved in 5478 iterations and 2.58 seconds (0.70 work units) Optimal objective -2.072293976e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
4804 -5.5022305e+09 0.000000e+00 0.000000e+00 3s
Solved in 4804 iterations and 2.86 seconds (0.95 work units)
Optimal objective -5.502230538e+09
5121 -4.8801711e+09 0.000000e+00 0.000000e+00 4s Solved in 5121 iterations and 3.53 seconds (1.09 work units) Optimal objective -4.880171132e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-jbfdn2ov.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x17659491
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
6002 1.3296166e+09 1.455664e+07 0.000000e+00 5s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.8323178e+09 7.368053e+06 0.000000e+00 0s
Warning: environment still referenced so free is deferred (Continue to use WLS)
5648 -3.9685101e+09 1.116339e+08 0.000000e+00 5s
Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-htyvt8yz.lp
Reading time = 0.20 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x943442c2
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [9e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.2021627e+31 4.202370e+28 9.202163e+01 0s
8225 1.6827699e+09 8.823670e+08 0.000000e+00 5s
7114 1.6324009e+09 0.000000e+00 0.000000e+00 7s Solved in 7114 iterations and 7.13 seconds (2.58 work units) Optimal objective 1.632400893e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
6875 -3.4223223e+09 0.000000e+00 0.000000e+00 7s
Solved in 6875 iterations and 7.48 seconds (2.67 work units)
Optimal objective -3.422322255e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
10984 3.1834181e+09 0.000000e+00 0.000000e+00 8s
Solved in 10984 iterations and 8.00 seconds (2.56 work units)
Optimal objective 3.183418052e+09
6484 7.4372884e+08 0.000000e+00 0.000000e+00 4s
Solved in 6484 iterations and 4.47 seconds (1.36 work units)
Optimal objective 7.437288371e+08
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
5405 -4.2327913e+09 2.714694e+10 0.000000e+00 5s
7454 -3.6156740e+09 0.000000e+00 0.000000e+00 8s Solved in 7454 iterations and 8.48 seconds (2.90 work units) Optimal objective -3.615673959e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model( /home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-nx1nz3rz.lp
Reading time = 0.10 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x284f4186
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3795530e+32 4.202370e+28 1.379553e+02 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-x8i8xgot.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x59fb2a95
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [9e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.9762840e+31 4.202370e+28 8.976284e+01 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-_k7b1hvr.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe376207a
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.7954920e+09 7.368053e+06 0.000000e+00 0s
6534 -1.7770498e+09 0.000000e+00 0.000000e+00 3s Solved in 6534 iterations and 2.86 seconds (0.93 work units) Optimal objective -1.777049783e+09
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-uzil6rjt.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe1a42e5a
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e+01, 8e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Warning: environment still referenced so free is deferred (Continue to use WLS)
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 7.365790e+06 0.000000e+00 0s
5918 -4.7641393e+09 2.760024e+09 0.000000e+00 5s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-4rqnz1ju.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xdfb74fc1
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
5528 -4.2184122e+09 1.091613e+08 0.000000e+00 5s
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 7.365790e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-qdz5gg0p.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x63dcd000
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.0795576e+32 4.202370e+28 1.079558e+02 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
7011 -4.5047542e+09 0.000000e+00 0.000000e+00 7s
Solved in 7011 iterations and 7.27 seconds (2.72 work units)
Optimal objective -4.504754157e+09
Read LP format model from file /tmp/linopy-problem-f_63kcll.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x375fff24
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e+01, 9e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -6.7613610e+31 4.202370e+28 6.761361e+01 0s
Warning: environment still referenced so free is deferred (Continue to use WLS)
7301 -2.6918470e+09 0.000000e+00 0.000000e+00 8s Solved in 7301 iterations and 8.31 seconds (2.85 work units) Optimal objective -2.691847043e+09
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Warning: environment still referenced so free is deferred (Continue to use WLS)
8421 5.5946717e+08 4.181005e+07 0.000000e+00 5s
8232 2.1466385e+09 3.982198e+08 0.000000e+00 5s
5254 -4.9529811e+09 0.000000e+00 0.000000e+00 3s
Solved in 5254 iterations and 3.15 seconds (1.04 work units)
Optimal objective -4.952981136e+09
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
5605 -5.5371137e+09 1.126010e+08 0.000000e+00 5s
Warning: environment still referenced so free is deferred (Continue to use WLS)
Read LP format model from file /tmp/linopy-problem-no149o4_.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xaf7a9eb5
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e+01, 6e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -6.4520199e+09 7.368053e+06 0.000000e+00 0s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
11859 1.7393073e+09 0.000000e+00 0.000000e+00 9s
Solved in 11859 iterations and 8.93 seconds (2.78 work units)
Optimal objective 1.739307334e+09
6880 -4.5170393e+09 0.000000e+00 0.000000e+00 8s
Solved in 6880 iterations and 7.55 seconds (2.57 work units)
Optimal objective -4.517039286e+09
10977 3.5459141e+09 0.000000e+00 0.000000e+00 9s Solved in 10977 iterations and 9.01 seconds (2.94 work units) Optimal objective 3.545914074e+09
Warning: environment still referenced so free is deferred (Continue to use WLS) Warning: environment still referenced so free is deferred (Continue to use WLS)
6244 -1.6777393e+09 0.000000e+00 0.000000e+00 4s Solved in 6244 iterations and 3.65 seconds (1.18 work units) Optimal objective -1.677739311e+09 Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-_w3sa9q8.lp
Reading time = 0.19 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x8a25bd1f
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [8e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.3492571e+09 9.633758e+06 0.000000e+00 0s
5680 -3.0824626e+09 0.000000e+00 0.000000e+00 2s Solved in 5680 iterations and 2.19 seconds (0.72 work units) Optimal objective -3.082462563e+09
Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de Warning: environment still referenced so free is deferred (Continue to use WLS)
Read LP format model from file /tmp/linopy-problem-nno0oypi.lp
Reading time = 0.23 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x26f54f24
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [8e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 7.365790e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-w3dyr2km.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb823599f
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e+00, 9e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -5.6910349e+30 4.202370e+28 5.691035e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-5a4sndum.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x1106f4fa
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e+00, 8e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.1202775e+10 9.633758e+06 0.000000e+00 0s
5895 -8.3634500e+08 0.000000e+00 0.000000e+00 3s Solved in 5895 iterations and 3.18 seconds (1.14 work units) Optimal objective -8.363450030e+08
8824 2.1425426e+09 2.149722e+08 0.000000e+00 5s
5519 -4.4683559e+09 0.000000e+00 0.000000e+00 2s
Solved in 5519 iterations and 1.94 seconds (0.64 work units)
Optimal objective -4.468355885e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-ih0i_2nt.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xd48c1150
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.08s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.4461244e+32 4.202370e+28 1.446124e+02 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-cfcrgomi.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x57298375
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [3e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Read LP format model from file /tmp/linopy-problem-boor2j09.lp
Reading time = 0.15 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x222093f1
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.1737457e+09 7.368053e+06 0.000000e+00 0s
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.4135169e+09 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-delco3r3.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xfeb70205
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.1756256e+32 4.202370e+28 1.175626e+02 0s
11661 2.9372647e+09 0.000000e+00 0.000000e+00 8s Solved in 11661 iterations and 8.11 seconds (2.95 work units) Optimal objective 2.937264728e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
5907 -1.0483469e+09 0.000000e+00 0.000000e+00 3s Solved in 5907 iterations and 2.82 seconds (0.88 work units) Optimal objective -1.048346933e+09
6527 2.4487493e+09 0.000000e+00 0.000000e+00 3s Solved in 6527 iterations and 3.40 seconds (1.10 work units) Optimal objective 2.448749308e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
5558 -4.8826336e+09 1.814503e+09 0.000000e+00 5s
6002 -5.5707283e+09 1.455664e+07 0.000000e+00 5s
6826 -4.5638988e+09 0.000000e+00 0.000000e+00 8s Solved in 6826 iterations and 7.70 seconds (2.62 work units) Optimal objective -4.563898841e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
7440 -5.2198016e+09 0.000000e+00 0.000000e+00 8s Solved in 7440 iterations and 7.93 seconds (2.73 work units) Optimal objective -5.219801564e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-03dc6rp2.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x703a53d2
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.5716456e+31 4.202370e+28 3.571646e+01 0s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
5402 -4.4939985e+09 0.000000e+00 0.000000e+00 2s Solved in 5402 iterations and 2.30 seconds (0.80 work units) Optimal objective -4.493998513e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-xlm8zi3f.lp
Reading time = 0.20 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x371072da
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e+01, 9e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.3212276e+31 4.202370e+28 7.321228e+01 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-gvo9wvfi.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x23871812
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e+01, 6e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.14s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.6014085e+09 7.368053e+06 0.000000e+00 0s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-iy8mtppu.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xad8c0617
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [7e+01, 8e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -4.9170264e+09 7.368053e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
6436 -2.5410956e+09 0.000000e+00 0.000000e+00 3s
Solved in 6436 iterations and 3.45 seconds (1.18 work units)
Optimal objective -2.541095590e+09
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
5558 -8.6666223e+08 3.115061e+07 0.000000e+00 5s
Read LP format model from file /tmp/linopy-problem-2_pfhj4v.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x4defc872
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 7.365790e+06 0.000000e+00 0s
Warning: environment still referenced so free is deferred (Continue to use WLS)
5629 -1.8000341e+09 0.000000e+00 0.000000e+00 3s Solved in 5629 iterations and 2.79 seconds (0.83 work units) Optimal objective -1.800034101e+09 Set parameter WLSAccessID Set parameter WLSSecret Set parameter LicenseID to value 2537914 Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-p79k0ors.lp
Reading time = 0.22 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x7eed2cb3
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.4894452e+09 7.368053e+06 0.000000e+00 0s
6947 -4.1399499e+08 0.000000e+00 0.000000e+00 8s Solved in 6947 iterations and 8.09 seconds (2.69 work units) Optimal objective -4.139949893e+08 Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Warning: environment still referenced so free is deferred (Continue to use WLS)
Read LP format model from file /tmp/linopy-problem-_5t0f9w1.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xcc723f53
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.09s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3416657e+32 4.202370e+28 1.341666e+02 0s
6006 -4.2861045e+09 0.000000e+00 0.000000e+00 3s
Solved in 6006 iterations and 2.76 seconds (0.79 work units)
Optimal objective -4.286104499e+09
7910 1.7959703e+09 7.599116e+07 0.000000e+00 5s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-9zjj7uc8.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xe7512568
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [8e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.11s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.4678393e+31 4.202370e+28 8.467839e+01 0s
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-8_dzr7o4.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xb91a1d64
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.3364443e+09 7.368053e+06 0.000000e+00 0s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
5062 -5.0143401e+09 0.000000e+00 0.000000e+00 3s Solved in 5062 iterations and 2.75 seconds (0.93 work units) Optimal objective -5.014340105e+09
5768 -4.0204159e+09 7.296928e+07 0.000000e+00 5s 10198 2.1645404e+09 0.000000e+00 0.000000e+00 9s Solved in 10198 iterations and 9.41 seconds (2.80 work units) Optimal objective 2.164540414e+09 Warning: environment still referenced so free is deferred (Continue to use WLS)
5784 -4.0300044e+08 0.000000e+00 0.000000e+00 3s Solved in 5784 iterations and 2.73 seconds (0.83 work units) Optimal objective -4.030004370e+08
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Warning: environment still referenced so free is deferred (Continue to use WLS)
6952 -3.2243402e+09 0.000000e+00 0.000000e+00 8s Solved in 6952 iterations and 7.55 seconds (2.71 work units) Optimal objective -3.224340239e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-_jo5ziwh.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x9f8e42a8
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [4e+01, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.12s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -4.1568338e+31 4.202370e+28 4.156834e+01 0s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
5449 -4.4614694e+09 0.000000e+00 0.000000e+00 2s Solved in 5449 iterations and 2.44 seconds (0.86 work units) Optimal objective -4.461469358e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-lgycqowk.lp
Reading time = 0.13 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xbdfd1b2f
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -3.4276838e+09 9.633758e+06 0.000000e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-mpq59mxm.lp
Reading time = 0.17 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xbcc50bcb
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [2e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.7687875e+31 4.202370e+28 1.768788e+01 0s
5736 -3.4964398e+08 0.000000e+00 0.000000e+00 2s Solved in 5736 iterations and 2.08 seconds (0.71 work units) Optimal objective -3.496439842e+08
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-v6sxdiil.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x75e33efb
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [9e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -8.7535438e+09 9.633758e+06 0.000000e+00 0s
6826 -1.9589511e+09 0.000000e+00 0.000000e+00 2s Solved in 6826 iterations and 2.36 seconds (0.84 work units) Optimal objective -1.958951063e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
5648 1.0081970e+08 6.355323e+07 0.000000e+00 5s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-vcxo9m_z.lp
Reading time = 0.16 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xc50bcde9
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [9e+00, 5e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -9.3322470e+30 4.202370e+28 9.332247e+00 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-rftioral.lp
Reading time = 0.18 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x5c197bec
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e+01, 6e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.15s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -4.5571288e+31 4.202370e+28 4.557129e+01 0s
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-mda7gnhi.lp
Reading time = 0.14 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x4bed8884
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [1e+02, 2e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.13s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -1.3886694e+32 4.202370e+28 1.388669e+02 0s
7211 1.2588046e+09 0.000000e+00 0.000000e+00 8s Solved in 7211 iterations and 8.14 seconds (2.82 work units) Optimal objective 1.258804632e+09
5359 -1.5395821e+09 0.000000e+00 0.000000e+00 3s Solved in 5359 iterations and 2.85 seconds (1.09 work units) Optimal objective -1.539582079e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
5645 -1.8797599e+09 5.892477e+07 0.000000e+00 5s
5485 -5.2166999e+09 1.541971e+09 0.000000e+00 5s
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
6527 -4.8021026e+09 0.000000e+00 0.000000e+00 7s Solved in 6527 iterations and 7.19 seconds (2.44 work units) Optimal objective -4.802102580e+09
7514 -1.3354857e+09 0.000000e+00 0.000000e+00 8s Solved in 7514 iterations and 8.31 seconds (2.93 work units) Optimal objective -1.335485715e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
Warning: environment still referenced so free is deferred (Continue to use WLS)
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-6wweo5i1.lp
Reading time = 0.12 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0x99e4a7df
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [5e+01, 1e+05]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.10s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -7.5249862e+09 7.368053e+06 0.000000e+00 0s
6000 -4.0840446e+09 0.000000e+00 0.000000e+00 1s Solved in 6000 iterations and 1.49 seconds (0.85 work units) Optimal objective -4.084044601e+09
Warning: environment still referenced so free is deferred (Continue to use WLS)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/checkouts/latest/pypsa/optimization/mga.py:502: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable. m = self._n.optimize.create_model(
Set parameter WLSAccessID
Set parameter WLSSecret
Set parameter LicenseID to value 2537914
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Read LP format model from file /tmp/linopy-problem-z13aj5j9.lp
Reading time = 0.02 seconds
obj: 21435 rows, 9746 columns, 42400 nonzeros
Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04 LTS")
CPU model: AMD EPYC 7R13 Processor, instruction set [SSE2|AVX|AVX2]
Thread count: 1 physical cores, 2 logical processors, using up to 2 threads
Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de
Optimize a model with 21435 rows, 9746 columns and 42400 nonzeros (Min)
Model fingerprint: 0xcf7215c0
Model has 6 linear objective coefficients
Coefficient statistics:
Matrix range [1e-03, 2e+05]
Objective range [6e+01, 8e+04]
Bounds range [0e+00, 0e+00]
RHS range [5e+03, 8e+09]
Warning: Model contains large rhs
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 11188 rows and 1442 columns
Presolve time: 0.02s
Presolved: 10247 rows, 8304 columns, 29770 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 -5.9246445e+31 4.202370e+28 5.924645e+01 0s
5960 -1.9741920e+09 0.000000e+00 0.000000e+00 1s Solved in 5960 iterations and 0.59 seconds (1.25 work units) Optimal objective -1.974192028e+09 Warning: environment still referenced so free is deferred (Continue to use WLS)
In [11]:
Copied!
fig, ax = plt.subplots(figsize=(8, 6))
ax.scatter(
pts["wind"] / 1e6, pts["solar"] / 1e6, c=pts["storage"] / 1e6, cmap="viridis"
)
hull = ConvexHull(pts[["wind", "solar"]] / 1e6)
line_segments = [hull.points[simplex] for simplex in hull.simplices]
ax.add_collection(LineCollection(line_segments, colors="k", linestyle="solid"))
ax.axis("equal")
ax.set_xlabel("Wind investment (mEUR)")
ax.set_ylabel("Solar investment (mEUR)")
cbar = plt.colorbar(ax.collections[0], ax=ax)
cbar.set_label("Storage investment (mEUR)")
fig, ax = plt.subplots(figsize=(8, 6))
ax.scatter(
pts["wind"] / 1e6, pts["solar"] / 1e6, c=pts["storage"] / 1e6, cmap="viridis"
)
hull = ConvexHull(pts[["wind", "solar"]] / 1e6)
line_segments = [hull.points[simplex] for simplex in hull.simplices]
ax.add_collection(LineCollection(line_segments, colors="k", linestyle="solid"))
ax.axis("equal")
ax.set_xlabel("Wind investment (mEUR)")
ax.set_ylabel("Solar investment (mEUR)")
cbar = plt.colorbar(ax.collections[0], ax=ax)
cbar.set_label("Storage investment (mEUR)")
In the above example, we see that low investment in renewables necessitates higher investment in storage, while high investment in renewables excludes (via the total system cost bound) a high investment in storage.