.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/optimizers/plot_multistart_example.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_optimizers_plot_multistart_example.py: Multi-start optimization ======================== The optimization algorithm ``multistart`` generates starting points using a DOE algorithm and run a sub-optimization algorithm from each starting point. .. GENERATED FROM PYTHON SOURCE LINES 29-40 .. code-block:: Python from __future__ import annotations from gemseo import create_design_space from gemseo import create_discipline from gemseo import create_scenario from gemseo import execute_post from gemseo.algos.opt.multi_start.settings.multi_start_settings import ( MultiStart_Settings, ) .. GENERATED FROM PYTHON SOURCE LINES 41-43 First, we create the disciplines .. GENERATED FROM PYTHON SOURCE LINES 43-48 .. code-block:: Python objective = create_discipline("AnalyticDiscipline", expressions={"obj": "x**3-x+1"}) constraint = create_discipline( "AnalyticDiscipline", expressions={"cstr": "x**2+obj**2-1.5"} ) .. GENERATED FROM PYTHON SOURCE LINES 49-50 and the design space .. GENERATED FROM PYTHON SOURCE LINES 50-53 .. code-block:: Python design_space = create_design_space() design_space.add_variable("x", lower_bound=-1.5, upper_bound=1.5, value=1.5) .. GENERATED FROM PYTHON SOURCE LINES 54-56 Then, we define the MDO scenario .. GENERATED FROM PYTHON SOURCE LINES 56-62 .. code-block:: Python scenario = create_scenario( [objective, constraint], "obj", design_space, formulation_name="DisciplinaryOpt", ) .. GENERATED FROM PYTHON SOURCE LINES 63-65 Note that the formulation settings passed to :func:`.create_scenario` can be provided via a Pydantic model. For more information, see :ref:`formulation_settings`. .. GENERATED FROM PYTHON SOURCE LINES 65-68 .. code-block:: Python scenario.add_constraint("cstr", constraint_type="ineq") .. GENERATED FROM PYTHON SOURCE LINES 69-72 and execute it with the ``MultiStart`` optimization algorithm combining the local optimization algorithm SLSQP and the full-factorial DOE algorithm: .. GENERATED FROM PYTHON SOURCE LINES 72-82 .. code-block:: Python multistart_settings = MultiStart_Settings( max_iter=100, opt_algo_name="SLSQP", doe_algo_name="PYDOE_FULLFACT", n_start=10, # Set multistart_file_path to save the history of the local optima. multistart_file_path="multistart.hdf5", ) scenario.execute(multistart_settings) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 16:17:31: *** Start MDOScenario execution *** INFO - 16:17:31: MDOScenario INFO - 16:17:31: Disciplines: AnalyticDiscipline AnalyticDiscipline INFO - 16:17:31: MDO formulation: DisciplinaryOpt INFO - 16:17:31: Optimization problem: INFO - 16:17:31: minimize obj(x) INFO - 16:17:31: with respect to x INFO - 16:17:31: under the inequality constraints INFO - 16:17:31: cstr(x) <= 0 INFO - 16:17:31: over the design space: INFO - 16:17:31: +------+-------------+-------+-------------+-------+ INFO - 16:17:31: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:31: +------+-------------+-------+-------------+-------+ INFO - 16:17:31: | x | -1.5 | 1.5 | 1.5 | float | INFO - 16:17:31: +------+-------------+-------+-------------+-------+ INFO - 16:17:31: Solving optimization problem with algorithm MultiStart: INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.5 | 1.5 | float | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 473.18 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 682.11 it/sec, feas=False, obj=-0.267] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 803.20 it/sec, feas=False, obj=-0.809] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 862.18 it/sec, feas=False, obj=-0.868] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 830.52 it/sec, feas=False, obj=-0.872] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 806.42 it/sec, feas=False, obj=-0.265] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 794.44 it/sec, feas=False, obj=0.136] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 825.93 it/sec, feas=False, obj=0.579] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 778.15 it/sec, feas=False, obj=0.289] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 799.04 it/sec, feas=False, obj=1.25] WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: WARNING - 16:17:32: The solution is not feasible. INFO - 16:17:32: Objective: 0.2888129873625884 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = 0.1513713660745195 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.252181466244097 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.166666666666667 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 577.09 it/sec, feas=False, obj=0.579] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 633.44 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 735.50 it/sec, feas=False, obj=-0.267] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 782.05 it/sec, feas=False, obj=-0.809] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 813.04 it/sec, feas=False, obj=-0.868] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 783.93 it/sec, feas=False, obj=-0.874] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 749.29 it/sec, feas=False, obj=-0.266] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 741.27 it/sec, feas=False, obj=0.135] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 767.88 it/sec, feas=False, obj=0.577] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 761.06 it/sec, feas=False, obj=0.288] WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: WARNING - 16:17:32: The solution is not feasible. INFO - 16:17:32: Objective: 0.28811314244670916 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = 0.15144075010172386 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.252370379421043 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -0.8333333333333334 | 1.5 | float | INFO - 16:17:32: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 523.44 it/sec, feas=False, obj=1.25] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 697.25 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 675.85 it/sec, feas=False, obj=1.01] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 735.23 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 728.46 it/sec, feas=False, obj=0.819] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 758.24 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 743.71 it/sec, feas=False, obj=0.693] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 772.84 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 760.50 it/sec, feas=False, obj=0.584] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 784.72 it/sec, feas=False, obj=-0.875] WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: WARNING - 16:17:32: The solution is not feasible. INFO - 16:17:32: Objective: 0.5837798748832244 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = 0.19806414473664136 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.165017254128868 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -0.5 | 1.5 | float | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 581.01 it/sec, feas=False, obj=1.38] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 782.96 it/sec, feas=False, obj=2.88] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 765.57 it/sec, feas=False, obj=1.23] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 804.59 it/sec, feas=False, obj=2.87] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 749.25 it/sec, feas=True, obj=0.848] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 711.12 it/sec, feas=True, obj=0.658] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 685.30 it/sec, feas=True, obj=0.643] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 664.63 it/sec, feas=True, obj=0.616] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 649.25 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 632.60 it/sec, feas=True, obj=0.615] INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: INFO - 16:17:32: The solution is feasible. INFO - 16:17:32: Objective: 0.6150998219543254 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = -0.788285881879476 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.5773788419679762 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -0.1666666666666667 | 1.5 | float | INFO - 16:17:32: +------+-------------+---------------------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 555.46 it/sec, feas=True, obj=1.16] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 739.15 it/sec, feas=False, obj=2.87] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 723.03 it/sec, feas=True, obj=0.785] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 744.53 it/sec, feas=False, obj=2.88] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 707.85 it/sec, feas=True, obj=0.644] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 682.96 it/sec, feas=True, obj=0.624] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 659.44 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 650.95 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 646.37 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 640.74 it/sec, feas=True, obj=0.615] INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: INFO - 16:17:32: The solution is feasible. INFO - 16:17:32: Objective: 0.6150998205402495 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = -0.7883188793606977 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.5773502675245377 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.1666666666666667 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 593.34 it/sec, feas=True, obj=0.838] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 795.20 it/sec, feas=False, obj=2.88] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 781.60 it/sec, feas=True, obj=0.656] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 728.75 it/sec, feas=True, obj=0.639] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 693.34 it/sec, feas=True, obj=0.616] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 678.85 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 663.76 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 651.59 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 645.66 it/sec, feas=True, obj=0.615] INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:32: Solution: INFO - 16:17:32: The solution is feasible. INFO - 16:17:32: Objective: 0.6150998205402495 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = -0.7883188774386114 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.5773502691891133 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.5 | 1.5 | float | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 537.73 it/sec, feas=True, obj=0.625] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 733.98 it/sec, feas=False, obj=2.87] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 739.34 it/sec, feas=True, obj=0.616] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 690.05 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 661.15 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 649.76 it/sec, feas=True, obj=0.615] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 641.85 it/sec, feas=True, obj=0.615] INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver. INFO - 16:17:32: Solution: INFO - 16:17:32: The solution is feasible. INFO - 16:17:32: Objective: 0.6150998205402495 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = -0.78831887743932 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.5773502691884995 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.8333333333333335 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 513.88 it/sec, feas=True, obj=0.745] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 590.17 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 701.90 it/sec, feas=False, obj=-0.267] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 726.48 it/sec, feas=False, obj=-0.809] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 776.84 it/sec, feas=False, obj=-0.868] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 761.84 it/sec, feas=False, obj=-0.874] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 752.71 it/sec, feas=False, obj=-0.266] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 732.09 it/sec, feas=False, obj=0.135] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 738.55 it/sec, feas=False, obj=0.577] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 733.24 it/sec, feas=False, obj=0.288] INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: INFO - 16:17:32: The solution is feasible. INFO - 16:17:32: Objective: 0.7453703703703706 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = -0.2499785665294918 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.8333333333333335 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+-------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+-------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 1.166666666666667 | 1.5 | float | INFO - 16:17:32: +------+-------------+-------------------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 10%|█ | 1/10 [00:00<00:00, 504.49 it/sec, feas=False, obj=1.42] INFO - 16:17:32: 20%|██ | 2/10 [00:00<00:00, 587.97 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 30%|███ | 3/10 [00:00<00:00, 711.74 it/sec, feas=False, obj=-0.267] INFO - 16:17:32: 40%|████ | 4/10 [00:00<00:00, 784.90 it/sec, feas=False, obj=-0.809] INFO - 16:17:32: 50%|█████ | 5/10 [00:00<00:00, 824.38 it/sec, feas=False, obj=-0.868] INFO - 16:17:32: 60%|██████ | 6/10 [00:00<00:00, 791.38 it/sec, feas=False, obj=-0.874] INFO - 16:17:32: 70%|███████ | 7/10 [00:00<00:00, 777.09 it/sec, feas=False, obj=-0.266] INFO - 16:17:32: 80%|████████ | 8/10 [00:00<00:00, 768.21 it/sec, feas=False, obj=0.135] INFO - 16:17:32: 90%|█████████ | 9/10 [00:00<00:00, 795.20 it/sec, feas=False, obj=0.577] INFO - 16:17:32: 100%|██████████| 10/10 [00:00<00:00, 783.16 it/sec, feas=False, obj=0.288] WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: WARNING - 16:17:32: The solution is not feasible. INFO - 16:17:32: Objective: 0.28811314244698893 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = 0.1514407501016959 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.252370379420967 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: Optimization problem: INFO - 16:17:32: minimize obj(x) INFO - 16:17:32: with respect to x INFO - 16:17:32: under the inequality constraints INFO - 16:17:32: cstr(x) <= 0 INFO - 16:17:32: over the design space: INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 1.5 | 1.5 | float | INFO - 16:17:32: +------+-------------+-------+-------------+-------+ INFO - 16:17:32: Solving optimization problem with algorithm SLSQP: INFO - 16:17:32: 11%|█ | 1/9 [00:00<00:00, 460.71 it/sec, feas=False, obj=2.88] INFO - 16:17:32: 22%|██▏ | 2/9 [00:00<00:00, 564.62 it/sec, feas=False, obj=-0.875] INFO - 16:17:32: 33%|███▎ | 3/9 [00:00<00:00, 689.70 it/sec, feas=False, obj=-0.267] INFO - 16:17:32: 44%|████▍ | 4/9 [00:00<00:00, 761.04 it/sec, feas=False, obj=-0.809] INFO - 16:17:32: 56%|█████▌ | 5/9 [00:00<00:00, 806.60 it/sec, feas=False, obj=-0.868] INFO - 16:17:32: 67%|██████▋ | 6/9 [00:00<00:00, 792.18 it/sec, feas=False, obj=-0.874] INFO - 16:17:32: 78%|███████▊ | 7/9 [00:00<00:00, 779.24 it/sec, feas=False, obj=-0.266] INFO - 16:17:32: 89%|████████▉ | 8/9 [00:00<00:00, 766.07 it/sec, feas=False, obj=0.135] INFO - 16:17:32: 100%|██████████| 9/9 [00:00<00:00, 792.59 it/sec, feas=False, obj=0.577] WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: Maximum number of iterations reached. GEMSEO stopped the driver. INFO - 16:17:32: Solution: WARNING - 16:17:32: The solution is not feasible. INFO - 16:17:32: Objective: 0.13490034433852438 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = 0.1877267982258064 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+-------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+-------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | -1.29210243221006 | 1.5 | float | INFO - 16:17:32: +------+-------------+-------------------+-------------+-------+ WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. WARNING - 16:17:32: Optimization found no feasible point; the least infeasible point is selected. INFO - 16:17:32: Exporting the optimization problem to the file multistart.hdf5 INFO - 16:17:32: 1%| | 1/100 [00:00<00:20, 4.91 it/sec, feas=False, obj=0.577] INFO - 16:17:32: Optimization result: INFO - 16:17:32: Optimizer info: INFO - 16:17:32: Status: None INFO - 16:17:32: Message: None INFO - 16:17:32: Solution: INFO - 16:17:32: The solution is feasible. INFO - 16:17:32: Objective: 0.6150998205402495 INFO - 16:17:32: Standardized constraints: INFO - 16:17:32: cstr = -0.7883188793606977 INFO - 16:17:32: Design space: INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | Name | Lower bound | Value | Upper bound | Type | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: | x | -1.5 | 0.5773502675245377 | 1.5 | float | INFO - 16:17:32: +------+-------------+--------------------+-------------+-------+ INFO - 16:17:32: *** End MDOScenario execution *** .. GENERATED FROM PYTHON SOURCE LINES 83-86 Lastly, we can plot the history of the objective, either by concatenating the 10 sub-optimization histories: .. GENERATED FROM PYTHON SOURCE LINES 86-90 .. code-block:: Python execute_post( scenario, post_name="BasicHistory", variable_names=["obj"], save=False, show=True ) .. image-sg:: /examples/optimizers/images/sphx_glr_plot_multistart_example_001.png :alt: History plot :srcset: /examples/optimizers/images/sphx_glr_plot_multistart_example_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 91-92 or by filtering the local optima (one per starting point): .. GENERATED FROM PYTHON SOURCE LINES 92-99 .. code-block:: Python execute_post( "multistart.hdf5", post_name="BasicHistory", variable_names=["obj"], save=False, show=True, ) .. image-sg:: /examples/optimizers/images/sphx_glr_plot_multistart_example_002.png :alt: History plot :srcset: /examples/optimizers/images/sphx_glr_plot_multistart_example_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 16:17:32: Importing the optimization problem from the file multistart.hdf5 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.523 seconds) .. _sphx_glr_download_examples_optimizers_plot_multistart_example.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_multistart_example.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_multistart_example.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_multistart_example.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_