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 configure_logger
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,
)
configure_logger()
<RootLogger root (INFO)>
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 - 11:44:05: *** Start MDOScenario execution ***
INFO - 11:44:05: MDOScenario
INFO - 11:44:05: Disciplines: AnalyticDiscipline AnalyticDiscipline
INFO - 11:44:05: MDO formulation: DisciplinaryOpt
INFO - 11:44:05: Optimization problem:
INFO - 11:44:05: minimize obj(x)
INFO - 11:44:05: with respect to x
INFO - 11:44:05: subject to constraints:
INFO - 11:44:05: cstr(x) <= 0
INFO - 11:44:05: over the design space:
INFO - 11:44:05: +------+-------------+-------+-------------+-------+
INFO - 11:44:05: | Name | Lower bound | Value | Upper bound | Type |
INFO - 11:44:05: +------+-------------+-------+-------------+-------+
INFO - 11:44:05: | x | -1.5 | 1.5 | 1.5 | float |
INFO - 11:44:05: +------+-------------+-------+-------------+-------+
INFO - 11:44:05: Solving optimization problem with algorithm MultiStart:
INFO - 11:44:05: 1%| | 1/100 [00:00<00:00, 280.54 it/sec, obj=2.88]
INFO - 11:44:05: 2%|▏ | 2/100 [00:00<00:00, 364.93 it/sec, obj=-0.875]
INFO - 11:44:05: 3%|▎ | 3/100 [00:00<00:00, 389.64 it/sec, obj=-0.267]
INFO - 11:44:05: 4%|▍ | 4/100 [00:00<00:00, 470.66 it/sec, obj=-0.809]
INFO - 11:44:05: 5%|▌ | 5/100 [00:00<00:00, 537.13 it/sec, obj=-0.868]
INFO - 11:44:05: 6%|▌ | 6/100 [00:00<00:00, 594.30 it/sec, obj=-0.872]
INFO - 11:44:05: 7%|▋ | 7/100 [00:00<00:00, 606.34 it/sec, obj=-0.265]
INFO - 11:44:05: 8%|▊ | 8/100 [00:00<00:00, 617.90 it/sec, obj=0.136]
INFO - 11:44:05: 9%|▉ | 9/100 [00:00<00:00, 626.66 it/sec, obj=0.579]
INFO - 11:44:05: 10%|█ | 10/100 [00:00<00:00, 658.67 it/sec, obj=0.289]
INFO - 11:44:05: 11%|█ | 11/100 [00:00<00:00, 662.30 it/sec, obj=1.25]
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
INFO - 11:44:05: 12%|█▏ | 12/100 [00:00<00:00, 641.72 it/sec, obj=0.579]
INFO - 11:44:05: 13%|█▎ | 13/100 [00:00<00:00, 633.51 it/sec, obj=-0.875]
INFO - 11:44:05: 14%|█▍ | 14/100 [00:00<00:00, 640.19 it/sec, obj=-0.267]
INFO - 11:44:05: 15%|█▌ | 15/100 [00:00<00:00, 660.48 it/sec, obj=-0.809]
INFO - 11:44:05: 16%|█▌ | 16/100 [00:00<00:00, 680.38 it/sec, obj=-0.868]
INFO - 11:44:05: 17%|█▋ | 17/100 [00:00<00:00, 697.61 it/sec, obj=-0.874]
INFO - 11:44:05: 18%|█▊ | 18/100 [00:00<00:00, 696.59 it/sec, obj=-0.266]
INFO - 11:44:05: 19%|█▉ | 19/100 [00:00<00:00, 693.22 it/sec, obj=0.135]
INFO - 11:44:05: 20%|██ | 20/100 [00:00<00:00, 693.28 it/sec, obj=0.577]
INFO - 11:44:05: 21%|██ | 21/100 [00:00<00:00, 707.23 it/sec, obj=0.288]
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
INFO - 11:44:05: 22%|██▏ | 22/100 [00:00<00:00, 679.18 it/sec, obj=1.25]
INFO - 11:44:05: 23%|██▎ | 23/100 [00:00<00:00, 673.09 it/sec, obj=-0.875]
INFO - 11:44:05: 24%|██▍ | 24/100 [00:00<00:00, 687.03 it/sec, obj=1.01]
INFO - 11:44:05: 25%|██▌ | 25/100 [00:00<00:00, 687.17 it/sec, obj=-0.875]
INFO - 11:44:05: 26%|██▌ | 26/100 [00:00<00:00, 699.24 it/sec, obj=0.819]
INFO - 11:44:05: 27%|██▋ | 27/100 [00:00<00:00, 699.90 it/sec, obj=-0.875]
INFO - 11:44:05: 28%|██▊ | 28/100 [00:00<00:00, 710.55 it/sec, obj=0.693]
INFO - 11:44:05: 29%|██▉ | 29/100 [00:00<00:00, 706.19 it/sec, obj=0.584]
INFO - 11:44:05: 30%|███ | 30/100 [00:00<00:00, 705.97 it/sec, obj=-0.875]
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
INFO - 11:44:05: 31%|███ | 31/100 [00:00<00:00, 696.67 it/sec, obj=1.38]
INFO - 11:44:05: 32%|███▏ | 32/100 [00:00<00:00, 688.12 it/sec, obj=1.23]
INFO - 11:44:05: 33%|███▎ | 33/100 [00:00<00:00, 688.83 it/sec, obj=2.87]
INFO - 11:44:05: 34%|███▍ | 34/100 [00:00<00:00, 697.39 it/sec, obj=0.848]
INFO - 11:44:05: 35%|███▌ | 35/100 [00:00<00:00, 696.63 it/sec, obj=0.658]
INFO - 11:44:05: 36%|███▌ | 36/100 [00:00<00:00, 689.96 it/sec, obj=0.643]
INFO - 11:44:05: 37%|███▋ | 37/100 [00:00<00:00, 684.12 it/sec, obj=0.616]
INFO - 11:44:05: 38%|███▊ | 38/100 [00:00<00:00, 678.30 it/sec, obj=0.615]
INFO - 11:44:05: 39%|███▉ | 39/100 [00:00<00:00, 672.84 it/sec, obj=0.615]
INFO - 11:44:05: 40%|████ | 40/100 [00:00<00:00, 658.10 it/sec, obj=1.16]
INFO - 11:44:05: 41%|████ | 41/100 [00:00<00:00, 652.69 it/sec, obj=2.87]
INFO - 11:44:05: 42%|████▏ | 42/100 [00:00<00:00, 657.85 it/sec, obj=0.785]
INFO - 11:44:05: 43%|████▎ | 43/100 [00:00<00:00, 648.45 it/sec, obj=0.644]
INFO - 11:44:05: 44%|████▍ | 44/100 [00:00<00:00, 644.99 it/sec, obj=0.624]
INFO - 11:44:05: 45%|████▌ | 45/100 [00:00<00:00, 641.31 it/sec, obj=0.615]
INFO - 11:44:05: 46%|████▌ | 46/100 [00:00<00:00, 638.20 it/sec, obj=0.615]
INFO - 11:44:05: 47%|████▋ | 47/100 [00:00<00:00, 635.25 it/sec, obj=0.615]
INFO - 11:44:05: 48%|████▊ | 48/100 [00:00<00:00, 631.24 it/sec, obj=0.615]
INFO - 11:44:05: 49%|████▉ | 49/100 [00:00<00:00, 620.54 it/sec, obj=0.838]
INFO - 11:44:05: 50%|█████ | 50/100 [00:00<00:00, 615.70 it/sec, obj=0.656]
INFO - 11:44:05: 51%|█████ | 51/100 [00:00<00:00, 613.08 it/sec, obj=0.639]
INFO - 11:44:05: 52%|█████▏ | 52/100 [00:00<00:00, 610.65 it/sec, obj=0.616]
INFO - 11:44:05: 53%|█████▎ | 53/100 [00:00<00:00, 608.31 it/sec, obj=0.615]
INFO - 11:44:05: 54%|█████▍ | 54/100 [00:00<00:00, 606.45 it/sec, obj=0.615]
INFO - 11:44:05: 55%|█████▌ | 55/100 [00:00<00:00, 604.78 it/sec, obj=0.615]
INFO - 11:44:05: 56%|█████▌ | 56/100 [00:00<00:00, 603.31 it/sec, obj=0.615]
INFO - 11:44:05: 57%|█████▋ | 57/100 [00:00<00:00, 601.62 it/sec, obj=0.615]
INFO - 11:44:05: 58%|█████▊ | 58/100 [00:00<00:00, 597.28 it/sec, obj=0.625]
INFO - 11:44:05: 59%|█████▉ | 59/100 [00:00<00:00, 594.85 it/sec, obj=2.87]
INFO - 11:44:05: 60%|██████ | 60/100 [00:00<00:00, 598.26 it/sec, obj=0.616]
INFO - 11:44:05: 61%|██████ | 61/100 [00:00<00:00, 596.80 it/sec, obj=0.615]
INFO - 11:44:05: 62%|██████▏ | 62/100 [00:00<00:00, 595.19 it/sec, obj=0.615]
INFO - 11:44:05: 63%|██████▎ | 63/100 [00:00<00:00, 593.62 it/sec, obj=0.615]
INFO - 11:44:05: 64%|██████▍ | 64/100 [00:00<00:00, 592.61 it/sec, obj=0.615]
INFO - 11:44:05: 65%|██████▌ | 65/100 [00:00<00:00, 591.39 it/sec, obj=0.615]
INFO - 11:44:05: 66%|██████▌ | 66/100 [00:00<00:00, 593.44 it/sec, obj=0.615]
INFO - 11:44:05: 67%|██████▋ | 67/100 [00:00<00:00, 593.31 it/sec, obj=0.745]
INFO - 11:44:05: 68%|██████▊ | 68/100 [00:00<00:00, 591.06 it/sec, obj=-0.875]
INFO - 11:44:05: 69%|██████▉ | 69/100 [00:00<00:00, 591.03 it/sec, obj=-0.267]
INFO - 11:44:05: 70%|███████ | 70/100 [00:00<00:00, 592.70 it/sec, obj=-0.809]
INFO - 11:44:05: 71%|███████ | 71/100 [00:00<00:00, 596.97 it/sec, obj=-0.868]
INFO - 11:44:05: 72%|███████▏ | 72/100 [00:00<00:00, 601.31 it/sec, obj=-0.874]
INFO - 11:44:05: 73%|███████▎ | 73/100 [00:00<00:00, 602.49 it/sec, obj=-0.266]
INFO - 11:44:05: 74%|███████▍ | 74/100 [00:00<00:00, 603.72 it/sec, obj=0.135]
INFO - 11:44:05: 75%|███████▌ | 75/100 [00:00<00:00, 604.61 it/sec, obj=0.577]
INFO - 11:44:05: 76%|███████▌ | 76/100 [00:00<00:00, 608.61 it/sec, obj=0.288]
INFO - 11:44:05: 77%|███████▋ | 77/100 [00:00<00:00, 604.57 it/sec, obj=1.42]
INFO - 11:44:05: 78%|███████▊ | 78/100 [00:00<00:00, 603.89 it/sec, obj=-0.875]
INFO - 11:44:05: 79%|███████▉ | 79/100 [00:00<00:00, 605.37 it/sec, obj=-0.267]
INFO - 11:44:05: 80%|████████ | 80/100 [00:00<00:00, 609.18 it/sec, obj=-0.809]
INFO - 11:44:05: 81%|████████ | 81/100 [00:00<00:00, 613.20 it/sec, obj=-0.868]
INFO - 11:44:05: 82%|████████▏ | 82/100 [00:00<00:00, 616.92 it/sec, obj=-0.874]
INFO - 11:44:05: 83%|████████▎ | 83/100 [00:00<00:00, 617.93 it/sec, obj=-0.266]
INFO - 11:44:05: 84%|████████▍ | 84/100 [00:00<00:00, 618.96 it/sec, obj=0.135]
INFO - 11:44:05: 85%|████████▌ | 85/100 [00:00<00:00, 620.18 it/sec, obj=0.577]
INFO - 11:44:05: 86%|████████▌ | 86/100 [00:00<00:00, 623.69 it/sec, obj=0.288]
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
INFO - 11:44:05: 87%|████████▋ | 87/100 [00:00<00:00, 610.26 it/sec, obj=-0.267]
INFO - 11:44:05: 88%|████████▊ | 88/100 [00:00<00:00, 613.68 it/sec, obj=-0.809]
INFO - 11:44:05: 89%|████████▉ | 89/100 [00:00<00:00, 617.23 it/sec, obj=-0.868]
INFO - 11:44:05: 90%|█████████ | 90/100 [00:00<00:00, 620.66 it/sec, obj=-0.874]
INFO - 11:44:05: 91%|█████████ | 91/100 [00:00<00:00, 621.50 it/sec, obj=-0.266]
INFO - 11:44:05: 92%|█████████▏| 92/100 [00:00<00:00, 622.58 it/sec, obj=0.135]
INFO - 11:44:05: 93%|█████████▎| 93/100 [00:00<00:00, 623.61 it/sec, obj=0.577]
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 11:44:05: Optimization found no feasible point; the least infeasible point is selected.
INFO - 11:44:05: Exporting the optimization problem to the file multistart.hdf5
INFO - 11:44:05: Optimization result:
INFO - 11:44:05: Optimizer info:
INFO - 11:44:05: Status: None
INFO - 11:44:05: Message: None
INFO - 11:44:05: Number of calls to the objective function by the optimizer: 1
INFO - 11:44:05: Solution:
INFO - 11:44:05: The solution is feasible.
INFO - 11:44:05: Objective: 0.6150998205402495
INFO - 11:44:05: Standardized constraints:
INFO - 11:44:05: cstr = -0.7883188793606977
INFO - 11:44:05: Design space:
INFO - 11:44:05: +------+-------------+--------------------+-------------+-------+
INFO - 11:44:05: | Name | Lower bound | Value | Upper bound | Type |
INFO - 11:44:05: +------+-------------+--------------------+-------------+-------+
INFO - 11:44:05: | x | -1.5 | 0.5773502675245377 | 1.5 | float |
INFO - 11:44:05: +------+-------------+--------------------+-------------+-------+
INFO - 11:44:05: *** End MDOScenario execution (time: 0:00:00.169368) ***
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 0x70492a4384a0>
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 - 11:44:05: Importing the optimization problem from the file multistart.hdf5
<gemseo.post.basic_history.BasicHistory object at 0x704947481cd0>
Total running time of the script: (0 minutes 0.550 seconds)