.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/multi_objective/plot_mnbi_fonseca.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_multi_objective_plot_mnbi_fonseca.py: Multi-objective Fonseca-Fleming example with the mNBI algorithm =============================================================== In this example, the modified Normal Boundary Intersection algorithm (mNBI) is used to solve the :class:`.FonsecaFleming` optimization problem :cite:`fonseca1995overview`: .. math:: \begin{aligned} \text{minimize the objective function } & f_1(x) = 1 - exp(-\sum_{i=1}^{d}((x_i - 1 / sqrt(d)) ^ 2)) \\ & f_2(x) = 1 + exp(-\sum_{i=1}^{d}((x_i + 1 / sqrt(d)) ^ 2)) \\ \text{with respect to the design variables }&x\\ \text{subject to the bound constraint} & x\in[-4,4]^d \end{aligned} We also show how the Pareto front can be refined. .. GENERATED FROM PYTHON SOURCE LINES 40-48 .. code-block:: Python from __future__ import annotations from gemseo import execute_algo from gemseo import execute_post from gemseo.problems.multiobjective_optimization.fonseca_fleming import FonsecaFleming from gemseo.settings.opt import MNBI_Settings .. GENERATED FROM PYTHON SOURCE LINES 49-55 Solve the Fonseca-Fleming optimization problem ---------------------------------------------- The 3 sub-optimization problems of mNBI are solved with SLSQP, a gradient-based optimization algorithm from the NLOPT library, with a maximum of 100 iterations. The analytic gradients are provided. .. GENERATED FROM PYTHON SOURCE LINES 55-63 .. code-block:: Python opt_problem = FonsecaFleming() mnbi_settings = MNBI_Settings( max_iter=1000, sub_optim_max_iter=100, n_sub_optim=3, sub_optim_algo="NLOPT_SLSQP", ) result = execute_algo(opt_problem, settings_model=mnbi_settings) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 16:17:17: Optimization problem: INFO - 16:17:17: minimize FonsecaFleming INFO - 16:17:17: with respect to x INFO - 16:17:17: over the design space: INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: Solving optimization problem with algorithm MNBI: INFO - 16:17:17: Searching for the individual optimum of each objective INFO - 16:17:17: Optimization problem: INFO - 16:17:17: minimize f_0 INFO - 16:17:17: with respect to x INFO - 16:17:17: over the design space: INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: 1%| | 6/1000 [00:00<00:01, 801.15 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]] INFO - 16:17:17: 1%| | 7/1000 [00:00<00:01, 791.02 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]] INFO - 16:17:17: 1%| | 8/1000 [00:00<00:01, 786.00 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]] INFO - 16:17:17: 1%| | 9/1000 [00:00<00:01, 780.61 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]] INFO - 16:17:17: 1%| | 10/1000 [00:00<00:01, 787.83 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]] INFO - 16:17:17: 1%| | 11/1000 [00:00<00:01, 782.98 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]] INFO - 16:17:17: 1%| | 12/1000 [00:00<00:01, 778.63 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:17:17: 1%|▏ | 13/1000 [00:00<00:01, 777.54 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:17:17: Optimization result: INFO - 16:17:17: Optimizer info: INFO - 16:17:17: Status: None INFO - 16:17:17: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:17: Solution: INFO - 16:17:17: Objective: 0.0 INFO - 16:17:17: Design space: INFO - 16:17:17: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | 0.5773502690103198 | 4 | float | INFO - 16:17:17: | x[1] | -4 | 0.5773502690115331 | 4 | float | INFO - 16:17:17: | x[2] | -4 | 0.5773502690114345 | 4 | float | INFO - 16:17:17: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:17: Optimization problem: INFO - 16:17:17: minimize f_1 INFO - 16:17:17: with respect to x INFO - 16:17:17: over the design space: INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: 1%|▏ | 14/1000 [00:00<00:01, 650.20 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:17:17: 2%|▏ | 15/1000 [00:00<00:01, 664.88 it/sec, feas=True, obj=[1. 1.]] INFO - 16:17:17: 2%|▏ | 16/1000 [00:00<00:01, 672.87 it/sec, feas=True, obj=[0.99999998 0.9931056 ]] INFO - 16:17:17: 2%|▏ | 17/1000 [00:00<00:01, 675.89 it/sec, feas=True, obj=[0.99688636 0.14955784]] INFO - 16:17:17: 2%|▏ | 18/1000 [00:00<00:01, 679.15 it/sec, feas=True, obj=[0.9492493 0.07206897]] INFO - 16:17:17: 2%|▏ | 19/1000 [00:00<00:01, 681.81 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]] INFO - 16:17:17: 2%|▏ | 20/1000 [00:00<00:01, 684.12 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]] INFO - 16:17:17: 2%|▏ | 21/1000 [00:00<00:01, 686.67 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]] INFO - 16:17:17: 2%|▏ | 22/1000 [00:00<00:01, 689.41 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]] INFO - 16:17:17: 2%|▏ | 23/1000 [00:00<00:01, 690.56 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]] INFO - 16:17:17: 2%|▏ | 24/1000 [00:00<00:01, 691.67 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]] INFO - 16:17:17: 2%|▎ | 25/1000 [00:00<00:01, 693.73 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:17:17: 3%|▎ | 26/1000 [00:00<00:01, 695.22 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:17:17: Optimization result: INFO - 16:17:17: Optimizer info: INFO - 16:17:17: Status: None INFO - 16:17:17: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:17: Solution: INFO - 16:17:17: Objective: 0.0 INFO - 16:17:17: Design space: INFO - 16:17:17: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | -0.5773502690171886 | 4 | float | INFO - 16:17:17: | x[1] | -4 | -0.5773502690183139 | 4 | float | INFO - 16:17:17: | x[2] | -4 | -0.5773502690182495 | 4 | float | INFO - 16:17:17: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:17: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218] INFO - 16:17:17: Optimization problem: INFO - 16:17:17: minimize -t_extraction INFO - 16:17:17: with respect to t, x INFO - 16:17:17: under the inequality constraints INFO - 16:17:17: beta_sub_optim_constraint <= 0.0 INFO - 16:17:17: over the design space: INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:17: | t | -inf | 0 | inf | float | INFO - 16:17:17: +------+-------------+-------+-------------+-------+ INFO - 16:17:17: 3%|▎ | 27/1000 [00:00<00:01, 613.89 it/sec, feas=True, obj=[0.98168436 0. ]] ERROR - 16:17:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited Traceback (most recent call last): File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.3.3/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run nlopt_problem.optimize(x_0.real) File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.3.3/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize return _nlopt.opt_optimize(self, *args) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ nlopt.RoundoffLimited: NLopt roundoff-limited INFO - 16:17:17: Optimization result: INFO - 16:17:17: Optimizer info: INFO - 16:17:17: Status: None INFO - 16:17:17: Message: GEMSEO stopped the driver. INFO - 16:17:17: Solution: INFO - 16:17:17: The solution is feasible. INFO - 16:17:17: Objective: 0.1439142599025487 INFO - 16:17:17: Standardized constraints: INFO - 16:17:17: beta_sub_optim_constraint = [ 4.99600361e-16 -1.33226763e-15] INFO - 16:17:17: Design space: INFO - 16:17:17: +------+-------------+------------------------+-------------+-------+ INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:17: +------+-------------+------------------------+-------------+-------+ INFO - 16:17:17: | x[0] | -4 | -2.193800696659309e-13 | 4 | float | INFO - 16:17:17: | x[1] | -4 | -2.193800696659309e-13 | 4 | float | INFO - 16:17:17: | x[2] | -4 | -2.193800696659309e-13 | 4 | float | INFO - 16:17:17: | t | -inf | -0.1439142599025487 | inf | float | INFO - 16:17:17: +------+-------------+------------------------+-------------+-------+ INFO - 16:17:18: 3%|▎ | 28/1000 [00:00<00:02, 452.42 it/sec, feas=True, obj=[0.63212056 0.63212056]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: None INFO - 16:17:18: Solution: INFO - 16:17:18: Objective: 0.8939534673502063 INFO - 16:17:18: Pareto efficient solutions: INFO - 16:17:18: Pareto optimal points : 8 / 28 INFO - 16:17:18: Utopia point : [0. 0.] INFO - 16:17:18: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]] INFO - 16:17:18: Distance from utopia : 0.8939534673502063 INFO - 16:17:18: Objective values: INFO - 16:17:18: +------+----------+----------+----------+ INFO - 16:17:18: | name | 1 | 2 | 3 | INFO - 16:17:18: +------+----------+----------+----------+ INFO - 16:17:18: | 1 | 0 | 0.981684 | 0.632121 | INFO - 16:17:18: | 2 | 0.981684 | 0 | 0.632121 | INFO - 16:17:18: +------+----------+----------+----------+ INFO - 16:17:18: Design space: INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:17:18: | name | lower_bound | 1 | 2 | 3 | upper_bound | type | INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:17:18: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:17:18: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:17:18: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+ .. GENERATED FROM PYTHON SOURCE LINES 64-70 Display the Pareto front ^^^^^^^^^^^^^^^^^^^^^^^^ |g| detects the Pareto optimal points and the dominated ones. The Fonseca-Fleming problem is interesting because its Pareto front is not convex. The mNBI algorithm successfully computes it. .. GENERATED FROM PYTHON SOURCE LINES 70-73 .. code-block:: Python execute_post(opt_problem, post_name="ParetoFront", save=False, show=True) .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_001.png :alt: Pareto front :srcset: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 74-77 Solve the Fonseca-Fleming optimization problem more finely ---------------------------------------------------------- The Pareto front is then refined with 10 sub-optimizations instead of 3. .. GENERATED FROM PYTHON SOURCE LINES 77-80 .. code-block:: Python opt_problem = FonsecaFleming() mnbi_settings.n_sub_optim = 10 result = execute_algo(opt_problem, settings_model=mnbi_settings) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize FonsecaFleming INFO - 16:17:18: with respect to x INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: Solving optimization problem with algorithm MNBI: INFO - 16:17:18: Searching for the individual optimum of each objective INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize f_0 INFO - 16:17:18: with respect to x INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: 1%| | 6/1000 [00:00<00:01, 812.43 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]] INFO - 16:17:18: 1%| | 7/1000 [00:00<00:01, 801.09 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]] INFO - 16:17:18: 1%| | 8/1000 [00:00<00:01, 793.85 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]] INFO - 16:17:18: 1%| | 9/1000 [00:00<00:01, 787.96 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]] INFO - 16:17:18: 1%| | 10/1000 [00:00<00:01, 792.20 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]] INFO - 16:17:18: 1%| | 11/1000 [00:00<00:01, 786.98 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]] INFO - 16:17:18: 1%| | 12/1000 [00:00<00:01, 781.37 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:17:18: 1%|▏ | 13/1000 [00:00<00:01, 779.74 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: Objective: 0.0 INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.5773502690103198 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.5773502690115331 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.5773502690114345 | 4 | float | INFO - 16:17:18: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize f_1 INFO - 16:17:18: with respect to x INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: 1%|▏ | 14/1000 [00:00<00:01, 646.39 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:17:18: 2%|▏ | 15/1000 [00:00<00:01, 660.49 it/sec, feas=True, obj=[1. 1.]] INFO - 16:17:18: 2%|▏ | 16/1000 [00:00<00:01, 669.40 it/sec, feas=True, obj=[0.99999998 0.9931056 ]] INFO - 16:17:18: 2%|▏ | 17/1000 [00:00<00:01, 672.60 it/sec, feas=True, obj=[0.99688636 0.14955784]] INFO - 16:17:18: 2%|▏ | 18/1000 [00:00<00:01, 676.37 it/sec, feas=True, obj=[0.9492493 0.07206897]] INFO - 16:17:18: 2%|▏ | 19/1000 [00:00<00:01, 679.38 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]] INFO - 16:17:18: 2%|▏ | 20/1000 [00:00<00:01, 681.90 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]] INFO - 16:17:18: 2%|▏ | 21/1000 [00:00<00:01, 684.46 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]] INFO - 16:17:18: 2%|▏ | 22/1000 [00:00<00:01, 687.54 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]] INFO - 16:17:18: 2%|▏ | 23/1000 [00:00<00:01, 693.38 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]] INFO - 16:17:18: 2%|▏ | 24/1000 [00:00<00:01, 693.79 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]] INFO - 16:17:18: 2%|▎ | 25/1000 [00:00<00:01, 695.80 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:17:18: 3%|▎ | 26/1000 [00:00<00:01, 698.13 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: Objective: 0.0 INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.5773502690171886 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.5773502690183139 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.5773502690182495 | 4 | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float | INFO - 16:17:18: | t | -inf | 0 | inf | float | INFO - 16:17:18: +------+-------------+-------+-------------+-------+ INFO - 16:17:18: 3%|▎ | 27/1000 [00:00<00:01, 616.92 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:17:18: 3%|▎ | 28/1000 [00:00<00:01, 621.06 it/sec, feas=True, obj=[0.90043834 0.20664322]] INFO - 16:17:18: 3%|▎ | 29/1000 [00:00<00:01, 619.89 it/sec, feas=True, obj=[0.91873293 0.15869784]] INFO - 16:17:18: 3%|▎ | 30/1000 [00:00<00:01, 619.39 it/sec, feas=True, obj=[0.91966962 0.15614908]] INFO - 16:17:18: 3%|▎ | 31/1000 [00:00<00:01, 619.05 it/sec, feas=True, obj=[0.91967277 0.15614049]] INFO - 16:17:18: 3%|▎ | 32/1000 [00:00<00:01, 618.82 it/sec, feas=True, obj=[0.91967277 0.15614049]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.04794255052713356 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [ 2.02608763e-13 -3.60156349e-13] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.3394642615047618 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.3394642612459058 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.3394642612538421 | 4 | float | INFO - 16:17:18: | t | -inf | -0.04794255052713356 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.3394642615047618 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.3394642612459058 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.3394642612538421 | 4 | float | INFO - 16:17:18: | t | -inf | -0.04794255052713356 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: 3%|▎ | 33/1000 [00:00<00:01, 559.90 it/sec, feas=True, obj=[0.91967277 0.15614049]] INFO - 16:17:18: 3%|▎ | 34/1000 [00:00<00:01, 564.13 it/sec, feas=True, obj=[0.84203912 0.33739501]] INFO - 16:17:18: 4%|▎ | 35/1000 [00:00<00:01, 564.23 it/sec, feas=True, obj=[0.85527677 0.31046303]] INFO - 16:17:18: 4%|▎ | 36/1000 [00:00<00:01, 564.73 it/sec, feas=True, obj=[0.85546004 0.31007996]] INFO - 16:17:18: 4%|▎ | 37/1000 [00:00<00:01, 565.41 it/sec, feas=True, obj=[0.85546007 0.31008016]] INFO - 16:17:18: 4%|▍ | 38/1000 [00:00<00:01, 569.30 it/sec, feas=True, obj=[0.85546004 0.31007996]] INFO - 16:17:18: 4%|▍ | 39/1000 [00:00<00:01, 568.86 it/sec, feas=True, obj=[0.85546004 0.31007996]] INFO - 16:17:18: 4%|▍ | 40/1000 [00:00<00:01, 570.17 it/sec, feas=True, obj=[0.85546007 0.3100799 ]] INFO - 16:17:18: 4%|▍ | 41/1000 [00:00<00:01, 571.13 it/sec, feas=True, obj=[0.85546007 0.31007989]] INFO - 16:17:18: 4%|▍ | 42/1000 [00:00<00:01, 572.78 it/sec, feas=True, obj=[0.855474 0.31005075]] INFO - 16:17:18: 4%|▍ | 43/1000 [00:00<00:01, 576.11 it/sec, feas=True, obj=[0.85546477 0.31007007]] INFO - 16:17:18: 4%|▍ | 44/1000 [00:00<00:01, 579.59 it/sec, feas=True, obj=[0.85546165 0.31007657]] INFO - 16:17:18: 4%|▍ | 45/1000 [00:00<00:01, 582.91 it/sec, feas=True, obj=[0.85546061 0.31007877]] INFO - 16:17:18: 5%|▍ | 46/1000 [00:00<00:01, 585.54 it/sec, feas=True, obj=[0.85546025 0.3100795 ]] INFO - 16:17:18: 5%|▍ | 47/1000 [00:00<00:01, 588.63 it/sec, feas=True, obj=[0.85546013 0.31007975]] INFO - 16:17:18: 5%|▍ | 48/1000 [00:00<00:01, 591.61 it/sec, feas=True, obj=[0.85546009 0.31007984]] INFO - 16:17:18: 5%|▍ | 49/1000 [00:00<00:01, 590.59 it/sec, feas=True, obj=[0.85546008 0.31007986]] INFO - 16:17:18: 5%|▌ | 50/1000 [00:00<00:01, 590.86 it/sec, feas=True, obj=[0.85546008 0.31007988]] INFO - 16:17:18: 5%|▌ | 51/1000 [00:00<00:01, 591.45 it/sec, feas=True, obj=[0.85546008 0.31007988]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.09363100822564815 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [ 2.56270122e-05 -1.74268465e-05] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.2256188538769552 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.225624434684276 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.2256242629358214 | 4 | float | INFO - 16:17:18: | t | -inf | -0.09363100822564815 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.2256188538769552 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.225624434684276 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.2256242629358214 | 4 | float | INFO - 16:17:18: | t | -inf | -0.09363100822564815 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: 5%|▌ | 52/1000 [00:00<00:01, 557.22 it/sec, feas=True, obj=[0.85546008 0.31007988]] INFO - 16:17:18: 5%|▌ | 53/1000 [00:00<00:01, 559.93 it/sec, feas=True, obj=[0.77161371 0.45984945]] INFO - 16:17:18: 5%|▌ | 54/1000 [00:00<00:01, 560.44 it/sec, feas=True, obj=[0.77769164 0.45052483]] INFO - 16:17:18: 6%|▌ | 55/1000 [00:00<00:01, 561.28 it/sec, feas=True, obj=[0.77768304 0.45048318]] INFO - 16:17:18: 6%|▌ | 56/1000 [00:00<00:01, 562.08 it/sec, feas=True, obj=[0.77769323 0.45046567]] INFO - 16:17:18: 6%|▌ | 57/1000 [00:00<00:01, 563.41 it/sec, feas=True, obj=[0.77769366 0.45046587]] INFO - 16:17:18: 6%|▌ | 58/1000 [00:00<00:01, 565.71 it/sec, feas=True, obj=[0.77769326 0.45046564]] INFO - 16:17:18: 6%|▌ | 59/1000 [00:00<00:01, 565.49 it/sec, feas=True, obj=[0.77769324 0.45046566]] INFO - 16:17:18: 6%|▌ | 60/1000 [00:00<00:01, 566.31 it/sec, feas=True, obj=[0.77769345 0.45046533]] INFO - 16:17:18: 6%|▌ | 61/1000 [00:00<00:01, 567.01 it/sec, feas=True, obj=[0.77769345 0.45046533]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.12550633340841144 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [1.91969087e-05 4.74588828e-05] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.1317111882954194 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.1300429705285642 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.1300943096640808 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1255063334084114 | inf | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.1317111882954194 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.1300429705285642 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.1300943096640808 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1255063334084114 | inf | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: 6%|▌ | 62/1000 [00:00<00:01, 533.98 it/sec, feas=True, obj=[0.77769345 0.45046533]] INFO - 16:17:18: 6%|▋ | 63/1000 [00:00<00:01, 536.28 it/sec, feas=True, obj=[0.68287184 0.58056149]] INFO - 16:17:18: 6%|▋ | 64/1000 [00:00<00:01, 537.42 it/sec, feas=True, obj=[0.71551876 0.62183493]] INFO - 16:17:18: 6%|▋ | 65/1000 [00:00<00:01, 537.65 it/sec, feas=True, obj=[0.6822982 0.57927725]] INFO - 16:17:18: 7%|▋ | 66/1000 [00:00<00:01, 539.63 it/sec, feas=True, obj=[0.68457659 0.57570624]] INFO - 16:17:18: 7%|▋ | 67/1000 [00:00<00:01, 540.39 it/sec, feas=True, obj=[0.68463465 0.57556826]] INFO - 16:17:18: 7%|▋ | 68/1000 [00:00<00:01, 541.24 it/sec, feas=True, obj=[0.68463912 0.57556308]] INFO - 16:17:18: 7%|▋ | 69/1000 [00:00<00:01, 542.16 it/sec, feas=True, obj=[0.68463912 0.57556308]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.14182402977147854 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [2.80166348e-05 3.76715222e-05] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.04284533444766803 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.04288451608870236 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.04288331028044423 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1418240297714785 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | -0.04284533444766803 | 4 | float | INFO - 16:17:18: | x[1] | -4 | -0.04288451608870236 | 4 | float | INFO - 16:17:18: | x[2] | -4 | -0.04288331028044423 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1418240297714785 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: 7%|▋ | 70/1000 [00:00<00:01, 523.07 it/sec, feas=True, obj=[0.68463912 0.57556308]] INFO - 16:17:18: 7%|▋ | 71/1000 [00:00<00:01, 525.27 it/sec, feas=True, obj=[0.57513208 0.68501203]] INFO - 16:17:18: 7%|▋ | 72/1000 [00:00<00:01, 526.02 it/sec, feas=True, obj=[0.57742427 0.68600327]] INFO - 16:17:18: 7%|▋ | 73/1000 [00:00<00:01, 527.02 it/sec, feas=True, obj=[0.57581454 0.68442239]] INFO - 16:17:18: 7%|▋ | 74/1000 [00:00<00:01, 527.72 it/sec, feas=True, obj=[0.5755631 0.6846391]] INFO - 16:17:18: 8%|▊ | 75/1000 [00:00<00:01, 528.59 it/sec, feas=True, obj=[0.57556308 0.68463912]] INFO - 16:17:18: 8%|▊ | 76/1000 [00:00<00:01, 529.91 it/sec, feas=True, obj=[0.57556312 0.68463915]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.1418570827634196 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [5.72929534e-08 2.36021925e-08] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.04289632102515561 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.04286361028511543 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.04286461695199684 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1418570827634196 | inf | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.04289632102515561 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.04286361028511543 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.04286461695199684 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1418570827634196 | inf | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: 8%|▊ | 77/1000 [00:00<00:01, 514.01 it/sec, feas=True, obj=[0.57556308 0.68463912]] INFO - 16:17:18: 8%|▊ | 78/1000 [00:00<00:01, 516.15 it/sec, feas=True, obj=[0.45294809 0.77609816]] INFO - 16:17:18: 8%|▊ | 79/1000 [00:00<00:01, 516.95 it/sec, feas=True, obj=[0.45218303 0.77835848]] INFO - 16:17:18: 8%|▊ | 80/1000 [00:00<00:01, 517.96 it/sec, feas=True, obj=[0.45106502 0.77730893]] INFO - 16:17:18: 8%|▊ | 81/1000 [00:00<00:01, 518.77 it/sec, feas=True, obj=[0.4504655 0.77769335]] INFO - 16:17:18: 8%|▊ | 82/1000 [00:00<00:01, 519.45 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:17:18: 8%|▊ | 83/1000 [00:00<00:01, 520.69 it/sec, feas=True, obj=[0.45046544 0.77769349]] INFO - 16:17:18: 8%|▊ | 84/1000 [00:00<00:01, 522.63 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:17:18: 8%|▊ | 85/1000 [00:00<00:01, 522.14 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.1255364904575047 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [1.05241364e-07 4.25739157e-08] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.1302782435029721 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.1308104725924997 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.1307940930583973 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1255364904575047 | inf | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.1302782435029721 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.1308104725924997 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.1307940930583973 | 4 | float | INFO - 16:17:18: | t | -inf | -0.1255364904575047 | inf | float | INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:18: 9%|▊ | 86/1000 [00:00<00:01, 507.22 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:17:18: 9%|▊ | 87/1000 [00:00<00:01, 509.13 it/sec, feas=True, obj=[0.31721618 0.85219022]] INFO - 16:17:18: 9%|▉ | 88/1000 [00:00<00:01, 510.27 it/sec, feas=True, obj=[0.55958733 0.90369381]] INFO - 16:17:18: 9%|▉ | 89/1000 [00:00<00:01, 510.48 it/sec, feas=True, obj=[0.31884168 0.85239351]] INFO - 16:17:18: 9%|▉ | 90/1000 [00:00<00:01, 512.08 it/sec, feas=True, obj=[0.31084099 0.85510192]] INFO - 16:17:18: 9%|▉ | 91/1000 [00:00<00:01, 512.85 it/sec, feas=True, obj=[0.31008381 0.85545831]] INFO - 16:17:18: 9%|▉ | 92/1000 [00:00<00:01, 513.65 it/sec, feas=True, obj=[0.31007993 0.85546005]] INFO - 16:17:18: 9%|▉ | 93/1000 [00:00<00:01, 514.55 it/sec, feas=True, obj=[0.31007988 0.85546007]] INFO - 16:17:18: 9%|▉ | 94/1000 [00:00<00:01, 515.44 it/sec, feas=True, obj=[0.31007988 0.85546008]] INFO - 16:17:18: 10%|▉ | 95/1000 [00:00<00:01, 516.35 it/sec, feas=True, obj=[0.31007988 0.85546008]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.09364002856425353 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [6.77503844e-06 1.07286382e-06] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.2252072104370182 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.2258054864979764 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.2257870743455523 | 4 | float | INFO - 16:17:18: | t | -inf | -0.09364002856425353 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832] INFO - 16:17:18: Optimization problem: INFO - 16:17:18: minimize -t_extraction INFO - 16:17:18: with respect to t, x INFO - 16:17:18: under the inequality constraints INFO - 16:17:18: beta_sub_optim_constraint <= 0.0 INFO - 16:17:18: over the design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.2252072104370182 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.2258054864979764 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.2257870743455523 | 4 | float | INFO - 16:17:18: | t | -inf | -0.09364002856425353 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: 10%|▉ | 96/1000 [00:00<00:01, 502.72 it/sec, feas=True, obj=[0.31007988 0.85546008]] INFO - 16:17:18: 10%|▉ | 97/1000 [00:00<00:01, 504.08 it/sec, feas=True, obj=[0.17176674 0.91401932]] INFO - 16:17:18: 10%|▉ | 98/1000 [00:00<00:01, 505.77 it/sec, feas=True, obj=[0.33992347 0.9334342 ]] INFO - 16:17:18: 10%|▉ | 99/1000 [00:00<00:01, 506.75 it/sec, feas=True, obj=[0.1717712 0.91427008]] INFO - 16:17:18: 10%|█ | 100/1000 [00:00<00:01, 508.19 it/sec, feas=True, obj=[0.15682461 0.91942509]] INFO - 16:17:18: 10%|█ | 101/1000 [00:00<00:01, 508.83 it/sec, feas=True, obj=[0.15614481 0.91967125]] INFO - 16:17:18: 10%|█ | 102/1000 [00:00<00:01, 509.64 it/sec, feas=True, obj=[0.15614056 0.91967275]] INFO - 16:17:18: 10%|█ | 103/1000 [00:00<00:01, 510.45 it/sec, feas=True, obj=[0.15614049 0.91967277]] INFO - 16:17:18: 10%|█ | 104/1000 [00:00<00:01, 511.51 it/sec, feas=True, obj=[0.15614049 0.91967277]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:18: Solution: INFO - 16:17:18: The solution is feasible. INFO - 16:17:18: Objective: 0.04794076312252382 INFO - 16:17:18: Standardized constraints: INFO - 16:17:18: beta_sub_optim_constraint = [6.07230357e-06 2.29674000e-07] INFO - 16:17:18: Design space: INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: | x[0] | -4 | 0.3391432958311196 | 4 | float | INFO - 16:17:18: | x[1] | -4 | 0.3396269686354314 | 4 | float | INFO - 16:17:18: | x[2] | -4 | 0.3396120834377401 | 4 | float | INFO - 16:17:18: | t | -inf | -0.04794076312252382 | inf | float | INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+ INFO - 16:17:18: 10%|█ | 105/1000 [00:00<00:01, 459.49 it/sec, feas=True, obj=[0.15614049 0.91967277]] INFO - 16:17:18: Optimization result: INFO - 16:17:18: Optimizer info: INFO - 16:17:18: Status: None INFO - 16:17:18: Message: None INFO - 16:17:18: Solution: INFO - 16:17:18: Objective: 0.8939534673502063 INFO - 16:17:18: Pareto efficient solutions: INFO - 16:17:18: Pareto optimal points : 66 / 105 INFO - 16:17:18: Utopia point : [0. 0.] INFO - 16:17:18: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]] INFO - 16:17:18: Distance from utopia : 0.8939534673502063 INFO - 16:17:18: Objective values: INFO - 16:17:18: +------+----------+----------+----------+ INFO - 16:17:18: | name | 1 | 2 | 3 | INFO - 16:17:18: +------+----------+----------+----------+ INFO - 16:17:18: | 1 | 0 | 0.981684 | 0.632121 | INFO - 16:17:18: | 2 | 0.981684 | 0 | 0.632121 | INFO - 16:17:18: +------+----------+----------+----------+ INFO - 16:17:18: Design space: INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:17:18: | name | lower_bound | 1 | 2 | 3 | upper_bound | type | INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:17:18: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:17:18: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:17:18: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+ .. GENERATED FROM PYTHON SOURCE LINES 81-84 Display the Pareto front ^^^^^^^^^^^^^^^^^^^^^^^^ We can clearly see the effect of the refinement. .. GENERATED FROM PYTHON SOURCE LINES 84-86 .. code-block:: Python execute_post(opt_problem, post_name="ParetoFront", save=False, show=True) .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_002.png :alt: Pareto front :srcset: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.588 seconds) .. _sphx_glr_download_examples_multi_objective_plot_mnbi_fonseca.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_mnbi_fonseca.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_mnbi_fonseca.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_mnbi_fonseca.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_