Note
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Multi-start optimization#
The optimization algorithm multistart
generates starting points using a DOE algorithm
and run a sub-optimization algorithm from each starting point.
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,
)
First, we create the disciplines
objective = create_discipline("AnalyticDiscipline", expressions={"obj": "x**3-x+1"})
constraint = create_discipline(
"AnalyticDiscipline", expressions={"cstr": "x**2+obj**2-1.5"}
)
and the design space
design_space = create_design_space()
design_space.add_variable("x", lower_bound=-1.5, upper_bound=1.5, value=1.5)
Then, we define the MDO scenario
scenario = create_scenario(
[objective, constraint],
"obj",
design_space,
formulation_name="DisciplinaryOpt",
)
Note that the formulation settings passed to create_scenario() can be provided
via a Pydantic model. For more information, see Formulation Settings.
scenario.add_constraint("cstr", constraint_type="ineq")
and execute it with the MultiStart optimization algorithm
combining the local optimization algorithm SLSQP
and the full-factorial DOE algorithm:
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)
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 ***
Lastly, we can plot the history of the objective, either by concatenating the 10 sub-optimization histories:
execute_post(
scenario, post_name="BasicHistory", variable_names=["obj"], save=False, show=True
)
<gemseo.post.basic_history.BasicHistory object at 0x7b1d43d08b00>
or by filtering the local optima (one per starting point):
execute_post(
"multistart.hdf5",
post_name="BasicHistory",
variable_names=["obj"],
save=False,
show=True,
)
INFO - 16:17:32: Importing the optimization problem from the file multistart.hdf5
<gemseo.post.basic_history.BasicHistory object at 0x7b1d2ed77d10>
Total running time of the script: (0 minutes 0.523 seconds)