.. 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 - 16:21:41: Optimization problem: INFO - 16:21:41: minimize FonsecaFleming INFO - 16:21:41: with respect to x INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: Solving optimization problem with algorithm MNBI: INFO - 16:21:41: Searching for the individual optimum of each objective INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize f_0 INFO - 16:21:41: with respect to x INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: 1%| | 6/1000 [00:00<00:00, 1176.69 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]] INFO - 16:21:41: 1%| | 7/1000 [00:00<00:00, 1185.07 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]] INFO - 16:21:41: 1%| | 8/1000 [00:00<00:00, 1195.55 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]] INFO - 16:21:41: 1%| | 9/1000 [00:00<00:00, 1203.30 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]] INFO - 16:21:41: 1%| | 10/1000 [00:00<00:00, 1224.51 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]] INFO - 16:21:41: 1%| | 11/1000 [00:00<00:00, 1227.64 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]] INFO - 16:21:41: 1%| | 12/1000 [00:00<00:00, 1228.23 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:21:41: 1%|▏ | 13/1000 [00:00<00:00, 1231.45 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: Objective: 0.0 INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.5773502690103198 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.5773502690115331 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.5773502690114345 | 4 | float | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize f_1 INFO - 16:21:41: with respect to x INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: 1%|▏ | 14/1000 [00:00<00:00, 1044.08 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:21:41: 2%|▏ | 15/1000 [00:00<00:00, 1067.94 it/sec, feas=True, obj=[1. 1.]] INFO - 16:21:41: 2%|▏ | 16/1000 [00:00<00:00, 1084.73 it/sec, feas=True, obj=[0.99999998 0.9931056 ]] INFO - 16:21:41: 2%|▏ | 17/1000 [00:00<00:00, 1091.88 it/sec, feas=True, obj=[0.99688636 0.14955784]] INFO - 16:21:41: 2%|▏ | 18/1000 [00:00<00:00, 1098.94 it/sec, feas=True, obj=[0.9492493 0.07206897]] INFO - 16:21:41: 2%|▏ | 19/1000 [00:00<00:00, 1106.03 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]] INFO - 16:21:41: 2%|▏ | 20/1000 [00:00<00:00, 1113.06 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]] INFO - 16:21:41: 2%|▏ | 21/1000 [00:00<00:00, 1118.99 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]] INFO - 16:21:41: 2%|▏ | 22/1000 [00:00<00:00, 1124.81 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]] INFO - 16:21:41: 2%|▏ | 23/1000 [00:00<00:00, 1135.45 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]] INFO - 16:21:41: 2%|▏ | 24/1000 [00:00<00:00, 1139.24 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]] INFO - 16:21:41: 2%|▎ | 25/1000 [00:00<00:00, 1144.55 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:21:41: 3%|▎ | 26/1000 [00:00<00:00, 1149.15 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: Objective: 0.0 INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.5773502690171886 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.5773502690183139 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.5773502690182495 | 4 | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: | t | -inf | 0 | inf | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: 3%|▎ | 27/1000 [00:00<00:00, 1017.51 it/sec, feas=True, obj=[0.98168436 0. ]] ERROR - 16:21:41: NLopt run failed: NLopt roundoff-limited, RoundoffLimited Traceback (most recent call last): File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.3.0/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/6.3.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize return _nlopt.opt_optimize(self, *args) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ nlopt.RoundoffLimited: NLopt roundoff-limited INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.1439142599025487 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [ 4.99600361e-16 -1.33226763e-15] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+------------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+------------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -2.193800696659309e-13 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -2.193800696659309e-13 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -2.193800696659309e-13 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1439142599025487 | inf | float | INFO - 16:21:41: +------+-------------+------------------------+-------------+-------+ INFO - 16:21:41: 3%|▎ | 28/1000 [00:00<00:01, 721.01 it/sec, feas=True, obj=[0.63212056 0.63212056]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: None INFO - 16:21:41: Solution: INFO - 16:21:41: Objective: 0.8939534673502063 INFO - 16:21:41: Pareto efficient solutions: INFO - 16:21:41: Pareto optimal points : 8 / 28 INFO - 16:21:41: Utopia point : [0. 0.] INFO - 16:21:41: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]] INFO - 16:21:41: Distance from utopia : 0.8939534673502063 INFO - 16:21:41: Objective values: INFO - 16:21:41: +------+----------+----------+----------+ INFO - 16:21:41: | name | 1 | 2 | 3 | INFO - 16:21:41: +------+----------+----------+----------+ INFO - 16:21:41: | 1 | 0 | 0.981684 | 0.632121 | INFO - 16:21:41: | 2 | 0.981684 | 0 | 0.632121 | INFO - 16:21:41: +------+----------+----------+----------+ INFO - 16:21:41: Design space: INFO - 16:21:41: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:21:41: | name | lower_bound | 1 | 2 | 3 | upper_bound | type | INFO - 16:21:41: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:21:41: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:21:41: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:21:41: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:21:41: +-------+-------------+---------+----------+---+-------------+-------+ .. 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 - 16:21:41: Optimization problem: INFO - 16:21:41: minimize FonsecaFleming INFO - 16:21:41: with respect to x INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: Solving optimization problem with algorithm MNBI: INFO - 16:21:41: Searching for the individual optimum of each objective INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize f_0 INFO - 16:21:41: with respect to x INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: 1%| | 6/1000 [00:00<00:00, 1264.04 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]] INFO - 16:21:41: 1%| | 7/1000 [00:00<00:00, 1264.43 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]] INFO - 16:21:41: 1%| | 8/1000 [00:00<00:00, 1265.15 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]] INFO - 16:21:41: 1%| | 9/1000 [00:00<00:00, 1265.97 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]] INFO - 16:21:41: 1%| | 10/1000 [00:00<00:00, 1283.01 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]] INFO - 16:21:41: 1%| | 11/1000 [00:00<00:00, 1279.39 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]] INFO - 16:21:41: 1%| | 12/1000 [00:00<00:00, 1281.65 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:21:41: 1%|▏ | 13/1000 [00:00<00:00, 1282.30 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: Objective: 0.0 INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.5773502690103198 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.5773502690115331 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.5773502690114345 | 4 | float | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize f_1 INFO - 16:21:41: with respect to x INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: 1%|▏ | 14/1000 [00:00<00:00, 1073.59 it/sec, feas=True, obj=[0. 0.98168436]] INFO - 16:21:41: 2%|▏ | 15/1000 [00:00<00:00, 1095.86 it/sec, feas=True, obj=[1. 1.]] INFO - 16:21:41: 2%|▏ | 16/1000 [00:00<00:00, 1113.54 it/sec, feas=True, obj=[0.99999998 0.9931056 ]] INFO - 16:21:41: 2%|▏ | 17/1000 [00:00<00:00, 1119.68 it/sec, feas=True, obj=[0.99688636 0.14955784]] INFO - 16:21:41: 2%|▏ | 18/1000 [00:00<00:00, 1126.49 it/sec, feas=True, obj=[0.9492493 0.07206897]] INFO - 16:21:41: 2%|▏ | 19/1000 [00:00<00:00, 1132.65 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]] INFO - 16:21:41: 2%|▏ | 20/1000 [00:00<00:00, 1139.96 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]] INFO - 16:21:41: 2%|▏ | 21/1000 [00:00<00:00, 1146.24 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]] INFO - 16:21:41: 2%|▏ | 22/1000 [00:00<00:00, 1152.08 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]] INFO - 16:21:41: 2%|▏ | 23/1000 [00:00<00:00, 1160.59 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]] INFO - 16:21:41: 2%|▏ | 24/1000 [00:00<00:00, 1162.88 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]] INFO - 16:21:41: 2%|▎ | 25/1000 [00:00<00:00, 1168.11 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:21:41: 3%|▎ | 26/1000 [00:00<00:00, 1172.42 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: Objective: 0.0 INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.5773502690171886 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.5773502690183139 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.5773502690182495 | 4 | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0 | 4 | float | INFO - 16:21:41: | t | -inf | 0 | inf | float | INFO - 16:21:41: +------+-------------+-------+-------------+-------+ INFO - 16:21:41: 3%|▎ | 27/1000 [00:00<00:00, 1039.78 it/sec, feas=True, obj=[0.98168436 0. ]] INFO - 16:21:41: 3%|▎ | 28/1000 [00:00<00:00, 1044.40 it/sec, feas=True, obj=[0.90043834 0.20664322]] INFO - 16:21:41: 3%|▎ | 29/1000 [00:00<00:00, 1041.02 it/sec, feas=True, obj=[0.91873293 0.15869784]] INFO - 16:21:41: 3%|▎ | 30/1000 [00:00<00:00, 1039.47 it/sec, feas=True, obj=[0.91966962 0.15614908]] INFO - 16:21:41: 3%|▎ | 31/1000 [00:00<00:00, 1036.71 it/sec, feas=True, obj=[0.91967277 0.15614049]] INFO - 16:21:41: 3%|▎ | 32/1000 [00:00<00:00, 1036.06 it/sec, feas=True, obj=[0.91967277 0.15614049]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.04794255052713356 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [ 2.02608763e-13 -3.60156349e-13] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.3394642615047618 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.3394642612459058 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.3394642612538421 | 4 | float | INFO - 16:21:41: | t | -inf | -0.04794255052713356 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.3394642615047618 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.3394642612459058 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.3394642612538421 | 4 | float | INFO - 16:21:41: | t | -inf | -0.04794255052713356 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: 3%|▎ | 33/1000 [00:00<00:01, 943.75 it/sec, feas=True, obj=[0.91967277 0.15614049]] INFO - 16:21:41: 3%|▎ | 34/1000 [00:00<00:01, 949.61 it/sec, feas=True, obj=[0.84203912 0.33739501]] INFO - 16:21:41: 4%|▎ | 35/1000 [00:00<00:01, 954.53 it/sec, feas=True, obj=[0.85527677 0.31046303]] INFO - 16:21:41: 4%|▎ | 36/1000 [00:00<00:01, 953.88 it/sec, feas=True, obj=[0.85546004 0.31007996]] INFO - 16:21:41: 4%|▎ | 37/1000 [00:00<00:01, 956.52 it/sec, feas=True, obj=[0.85546007 0.31008016]] INFO - 16:21:41: 4%|▍ | 38/1000 [00:00<00:00, 963.47 it/sec, feas=True, obj=[0.85546004 0.31007996]] INFO - 16:21:41: 4%|▍ | 39/1000 [00:00<00:00, 961.88 it/sec, feas=True, obj=[0.85546004 0.31007996]] INFO - 16:21:41: 4%|▍ | 40/1000 [00:00<00:00, 963.19 it/sec, feas=True, obj=[0.85546005 0.31007993]] INFO - 16:21:41: 4%|▍ | 41/1000 [00:00<00:00, 964.72 it/sec, feas=True, obj=[0.85546009 0.31007985]] INFO - 16:21:41: 4%|▍ | 42/1000 [00:00<00:00, 967.55 it/sec, feas=True, obj=[0.85546012 0.31007978]] INFO - 16:21:41: 4%|▍ | 43/1000 [00:00<00:00, 973.17 it/sec, feas=True, obj=[0.8554601 0.31007982]] INFO - 16:21:41: 4%|▍ | 44/1000 [00:00<00:00, 978.98 it/sec, feas=True, obj=[0.85546009 0.31007984]] INFO - 16:21:41: 4%|▍ | 45/1000 [00:00<00:00, 984.31 it/sec, feas=True, obj=[0.85546009 0.31007985]] INFO - 16:21:41: 5%|▍ | 46/1000 [00:00<00:00, 989.74 it/sec, feas=True, obj=[0.85546009 0.31007985]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.09364288152510496 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [ 8.90168644e-08 -5.43837472e-08] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.2256025800102535 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.2256025813833293 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.225602581344992 | 4 | float | INFO - 16:21:41: | t | -inf | -0.09364288152510496 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.2256025800102535 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.2256025813833293 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.225602581344992 | 4 | float | INFO - 16:21:41: | t | -inf | -0.09364288152510496 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: 5%|▍ | 47/1000 [00:00<00:01, 934.42 it/sec, feas=True, obj=[0.85546009 0.31007985]] INFO - 16:21:41: 5%|▍ | 48/1000 [00:00<00:01, 938.72 it/sec, feas=True, obj=[0.77161691 0.45984452]] INFO - 16:21:41: 5%|▍ | 49/1000 [00:00<00:01, 939.12 it/sec, feas=True, obj=[0.77767797 0.45048948]] INFO - 16:21:41: 5%|▌ | 50/1000 [00:00<00:01, 940.17 it/sec, feas=True, obj=[0.77769345 0.45046534]] INFO - 16:21:41: 5%|▌ | 51/1000 [00:00<00:01, 940.82 it/sec, feas=True, obj=[0.77769345 0.45046534]] INFO - 16:21:41: 5%|▌ | 52/1000 [00:00<00:01, 943.11 it/sec, feas=True, obj=[0.77769345 0.45046533]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.1255364919707028 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [-4.93896729e-11 3.78963430e-09] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.130635251180903 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.1306236158744216 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.1306239407408536 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1255364919707028 | inf | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.130635251180903 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.1306236158744216 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.1306239407408536 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1255364919707028 | inf | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: 5%|▌ | 53/1000 [00:00<00:01, 875.90 it/sec, feas=True, obj=[0.77769345 0.45046533]] INFO - 16:21:41: 5%|▌ | 54/1000 [00:00<00:01, 879.76 it/sec, feas=True, obj=[0.68170379 0.57895302]] INFO - 16:21:41: 6%|▌ | 55/1000 [00:00<00:01, 881.01 it/sec, feas=True, obj=[0.68474464 0.57570928]] INFO - 16:21:41: 6%|▌ | 56/1000 [00:00<00:01, 882.66 it/sec, feas=True, obj=[0.68462383 0.57558142]] INFO - 16:21:41: 6%|▌ | 57/1000 [00:00<00:01, 884.06 it/sec, feas=True, obj=[0.68463908 0.57556312]] INFO - 16:21:41: 6%|▌ | 58/1000 [00:00<00:01, 885.94 it/sec, feas=True, obj=[0.68463912 0.57556308]] INFO - 16:21:41: 6%|▌ | 59/1000 [00:00<00:01, 888.01 it/sec, feas=True, obj=[0.68463912 0.57556308]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.14185683491615905 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [2.43262084e-07 3.27480598e-07] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.04287461308631135 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.04287494223710642 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.04287493304700618 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1418568349161591 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | -0.04287461308631135 | 4 | float | INFO - 16:21:41: | x[1] | -4 | -0.04287494223710642 | 4 | float | INFO - 16:21:41: | x[2] | -4 | -0.04287493304700618 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1418568349161591 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: 6%|▌ | 60/1000 [00:00<00:01, 852.86 it/sec, feas=True, obj=[0.68463912 0.57556308]] INFO - 16:21:41: 6%|▌ | 61/1000 [00:00<00:01, 856.89 it/sec, feas=True, obj=[0.57513103 0.68501143]] INFO - 16:21:41: 6%|▌ | 62/1000 [00:00<00:01, 858.36 it/sec, feas=True, obj=[0.57556323 0.6846392 ]] INFO - 16:21:41: 6%|▋ | 63/1000 [00:00<00:01, 861.07 it/sec, feas=True, obj=[0.57572435 0.68475688]] INFO - 16:21:41: 6%|▋ | 64/1000 [00:00<00:01, 865.39 it/sec, feas=True, obj=[0.5755641 0.68463965]] INFO - 16:21:41: 6%|▋ | 65/1000 [00:00<00:01, 865.59 it/sec, feas=True, obj=[0.57556313 0.68463907]] INFO - 16:21:41: 7%|▋ | 66/1000 [00:00<00:01, 867.46 it/sec, feas=True, obj=[0.57556308 0.68463912]] INFO - 16:21:41: 7%|▋ | 67/1000 [00:00<00:01, 869.98 it/sec, feas=True, obj=[0.57556308 0.68463912]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.1418563998953318 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [1.73495133e-06 1.23800550e-06] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.04169925261518337 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.04348747161026356 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.04343754339469275 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1418563998953318 | inf | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.04169925261518337 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.04348747161026356 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.04343754339469275 | 4 | float | INFO - 16:21:41: | t | -inf | -0.1418563998953318 | inf | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: 7%|▋ | 68/1000 [00:00<00:01, 838.11 it/sec, feas=True, obj=[0.57556308 0.68463912]] INFO - 16:21:41: 7%|▋ | 69/1000 [00:00<00:01, 841.74 it/sec, feas=True, obj=[0.45538924 0.77708466]] INFO - 16:21:41: 7%|▋ | 70/1000 [00:00<00:01, 843.98 it/sec, feas=True, obj=[0.63252142 0.83907792]] INFO - 16:21:41: 7%|▋ | 71/1000 [00:00<00:01, 844.62 it/sec, feas=True, obj=[0.45487133 0.7750112 ]] INFO - 16:21:41: 7%|▋ | 72/1000 [00:00<00:01, 847.40 it/sec, feas=True, obj=[0.45051277 0.77766464]] INFO - 16:21:41: 7%|▋ | 73/1000 [00:00<00:01, 848.90 it/sec, feas=True, obj=[0.45046575 0.77769322]] INFO - 16:21:41: 7%|▋ | 74/1000 [00:00<00:01, 850.54 it/sec, feas=True, obj=[0.45046535 0.77769344]] INFO - 16:21:41: 8%|▊ | 75/1000 [00:00<00:01, 852.29 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:21:41: 8%|▊ | 76/1000 [00:00<00:01, 854.55 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.125535809547323 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [1.09187899e-06 4.40780275e-07] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.1304145607706708 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.1307382545134637 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.1307292167773948 | 4 | float | INFO - 16:21:41: | t | -inf | -0.125535809547323 | inf | float | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.1304145607706708 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.1307382545134637 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.1307292167773948 | 4 | float | INFO - 16:21:41: | t | -inf | -0.125535809547323 | inf | float | INFO - 16:21:41: +------+-------------+--------------------+-------------+-------+ INFO - 16:21:41: 8%|▊ | 77/1000 [00:00<00:01, 826.25 it/sec, feas=True, obj=[0.45046533 0.77769345]] INFO - 16:21:41: 8%|▊ | 78/1000 [00:00<00:01, 829.50 it/sec, feas=True, obj=[0.31706447 0.85215876]] INFO - 16:21:41: 8%|▊ | 79/1000 [00:00<00:01, 831.41 it/sec, feas=True, obj=[0.44069654 0.88070624]] INFO - 16:21:41: 8%|▊ | 80/1000 [00:00<00:01, 831.91 it/sec, feas=True, obj=[0.31749875 0.85247189]] INFO - 16:21:41: 8%|▊ | 81/1000 [00:00<00:01, 834.89 it/sec, feas=True, obj=[0.31049571 0.85526244]] INFO - 16:21:41: 8%|▊ | 82/1000 [00:00<00:01, 836.30 it/sec, feas=True, obj=[0.31008062 0.85545979]] INFO - 16:21:41: 8%|▊ | 83/1000 [00:00<00:01, 837.94 it/sec, feas=True, obj=[0.31007991 0.85546006]] INFO - 16:21:41: 8%|▊ | 84/1000 [00:00<00:01, 839.68 it/sec, feas=True, obj=[0.31007988 0.85546007]] INFO - 16:21:41: 8%|▊ | 85/1000 [00:00<00:01, 841.33 it/sec, feas=True, obj=[0.31007988 0.85546008]] INFO - 16:21:41: 9%|▊ | 86/1000 [00:00<00:01, 842.65 it/sec, feas=True, obj=[0.31007988 0.85546008]] ERROR - 16:21:41: NLopt run failed: NLopt roundoff-limited, RoundoffLimited Traceback (most recent call last): File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.3.0/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/6.3.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize return _nlopt.opt_optimize(self, *args) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ nlopt.RoundoffLimited: NLopt roundoff-limited INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.09364249860428303 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [1.16135075e-06 1.35331413e-07] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.2252840082297061 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.2257678647994927 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.2257543552148791 | 4 | float | INFO - 16:21:41: | t | -inf | -0.09364249860428303 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832] INFO - 16:21:41: Optimization problem: INFO - 16:21:41: minimize -t_extraction INFO - 16:21:41: with respect to t, x INFO - 16:21:41: under the inequality constraints INFO - 16:21:41: beta_sub_optim_constraint <= 0.0 INFO - 16:21:41: over the design space: INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.2252840082297061 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.2257678647994927 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.2257543552148791 | 4 | float | INFO - 16:21:41: | t | -inf | -0.09364249860428303 | inf | float | INFO - 16:21:41: +------+-------------+----------------------+-------------+-------+ INFO - 16:21:41: 9%|▊ | 87/1000 [00:00<00:01, 818.90 it/sec, feas=True, obj=[0.31007988 0.85546008]] INFO - 16:21:41: 9%|▉ | 88/1000 [00:00<00:01, 821.88 it/sec, feas=True, obj=[0.17166205 0.91400962]] INFO - 16:21:41: 9%|▉ | 89/1000 [00:00<00:01, 825.17 it/sec, feas=True, obj=[0.31290173 0.93170725]] INFO - 16:21:41: 9%|▉ | 90/1000 [00:00<00:01, 827.01 it/sec, feas=True, obj=[0.17159576 0.91440627]] INFO - 16:21:41: 9%|▉ | 91/1000 [00:00<00:01, 829.47 it/sec, feas=True, obj=[0.15690892 0.9193933 ]] INFO - 16:21:41: 9%|▉ | 92/1000 [00:00<00:01, 830.73 it/sec, feas=True, obj=[0.15614425 0.91967142]] INFO - 16:21:41: 9%|▉ | 93/1000 [00:00<00:01, 832.11 it/sec, feas=True, obj=[0.15614052 0.91967276]] INFO - 16:21:41: 9%|▉ | 94/1000 [00:00<00:01, 833.64 it/sec, feas=True, obj=[0.15614049 0.91967277]] INFO - 16:21:41: 10%|▉ | 95/1000 [00:00<00:01, 835.20 it/sec, feas=True, obj=[0.15614049 0.91967277]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:21:41: Solution: INFO - 16:21:41: The solution is feasible. INFO - 16:21:41: Objective: 0.0479411260233733 INFO - 16:21:41: Standardized constraints: INFO - 16:21:41: beta_sub_optim_constraint = [5.15990506e-06 4.55681550e-08] INFO - 16:21:41: Design space: INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: | x[0] | -4 | 0.3392459389454796 | 4 | float | INFO - 16:21:41: | x[1] | -4 | 0.3395733823668694 | 4 | float | INFO - 16:21:41: | x[2] | -4 | 0.3395642399370322 | 4 | float | INFO - 16:21:41: | t | -inf | -0.0479411260233733 | inf | float | INFO - 16:21:41: +------+-------------+---------------------+-------------+-------+ INFO - 16:21:41: 10%|▉ | 96/1000 [00:00<00:01, 735.84 it/sec, feas=True, obj=[0.15614049 0.91967277]] INFO - 16:21:41: Optimization result: INFO - 16:21:41: Optimizer info: INFO - 16:21:41: Status: None INFO - 16:21:41: Message: None INFO - 16:21:41: Solution: INFO - 16:21:41: Objective: 0.8939534673502063 INFO - 16:21:41: Pareto efficient solutions: INFO - 16:21:41: Pareto optimal points : 63 / 96 INFO - 16:21:41: Utopia point : [0. 0.] INFO - 16:21:41: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]] INFO - 16:21:41: Distance from utopia : 0.8939534673502063 INFO - 16:21:41: Objective values: INFO - 16:21:41: +------+----------+----------+----------+ INFO - 16:21:41: | name | 1 | 2 | 3 | INFO - 16:21:41: +------+----------+----------+----------+ INFO - 16:21:41: | 1 | 0 | 0.981684 | 0.632121 | INFO - 16:21:41: | 2 | 0.981684 | 0 | 0.632121 | INFO - 16:21:41: +------+----------+----------+----------+ INFO - 16:21:41: Design space: INFO - 16:21:41: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:21:41: | name | lower_bound | 1 | 2 | 3 | upper_bound | type | INFO - 16:21:41: +-------+-------------+---------+----------+---+-------------+-------+ INFO - 16:21:41: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:21:41: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:21:41: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float | INFO - 16:21:41: +-------+-------------+---------+----------+---+-------------+-------+ .. 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 0.388 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 `_