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 - 15:35:43: *** Start MDOScenario execution ***
INFO - 15:35:43: MDOScenario
INFO - 15:35:43: Disciplines: AnalyticDiscipline AnalyticDiscipline
INFO - 15:35:43: MDO formulation: DisciplinaryOpt
INFO - 15:35:43: Optimization problem:
INFO - 15:35:43: minimize obj(x)
INFO - 15:35:43: with respect to x
INFO - 15:35:43: subject to constraints:
INFO - 15:35:43: cstr(x) <= 0
INFO - 15:35:43: over the design space:
INFO - 15:35:43: +------+-------------+-------+-------------+-------+
INFO - 15:35:43: | Name | Lower bound | Value | Upper bound | Type |
INFO - 15:35:43: +------+-------------+-------+-------------+-------+
INFO - 15:35:43: | x | -1.5 | 1.5 | 1.5 | float |
INFO - 15:35:43: +------+-------------+-------+-------------+-------+
INFO - 15:35:43: Solving optimization problem with algorithm MultiStart:
INFO - 15:35:43: 1%| | 1/100 [00:00<00:00, 286.91 it/sec, obj=2.88]
INFO - 15:35:43: 2%|▏ | 2/100 [00:00<00:00, 375.36 it/sec, obj=-0.875]
INFO - 15:35:43: 3%|▎ | 3/100 [00:00<00:00, 402.09 it/sec, obj=-0.267]
INFO - 15:35:43: 4%|▍ | 4/100 [00:00<00:00, 485.52 it/sec, obj=-0.809]
INFO - 15:35:43: 5%|▌ | 5/100 [00:00<00:00, 553.08 it/sec, obj=-0.868]
INFO - 15:35:43: 6%|▌ | 6/100 [00:00<00:00, 612.90 it/sec, obj=-0.872]
INFO - 15:35:43: 7%|▋ | 7/100 [00:00<00:00, 625.90 it/sec, obj=-0.265]
INFO - 15:35:43: 8%|▊ | 8/100 [00:00<00:00, 636.19 it/sec, obj=0.136]
INFO - 15:35:43: 9%|▉ | 9/100 [00:00<00:00, 644.98 it/sec, obj=0.579]
INFO - 15:35:43: 10%|█ | 10/100 [00:00<00:00, 678.19 it/sec, obj=0.289]
INFO - 15:35:43: 11%|█ | 11/100 [00:00<00:00, 680.78 it/sec, obj=1.25]
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
INFO - 15:35:43: 12%|█▏ | 12/100 [00:00<00:00, 659.89 it/sec, obj=0.579]
INFO - 15:35:43: 13%|█▎ | 13/100 [00:00<00:00, 650.51 it/sec, obj=-0.875]
INFO - 15:35:43: 14%|█▍ | 14/100 [00:00<00:00, 656.79 it/sec, obj=-0.267]
INFO - 15:35:43: 15%|█▌ | 15/100 [00:00<00:00, 671.79 it/sec, obj=-0.809]
INFO - 15:35:43: 16%|█▌ | 16/100 [00:00<00:00, 688.12 it/sec, obj=-0.868]
INFO - 15:35:43: 17%|█▋ | 17/100 [00:00<00:00, 707.06 it/sec, obj=-0.874]
INFO - 15:35:43: 18%|█▊ | 18/100 [00:00<00:00, 708.56 it/sec, obj=-0.266]
INFO - 15:35:43: 19%|█▉ | 19/100 [00:00<00:00, 705.87 it/sec, obj=0.135]
INFO - 15:35:43: 20%|██ | 20/100 [00:00<00:00, 706.00 it/sec, obj=0.577]
INFO - 15:35:43: 21%|██ | 21/100 [00:00<00:00, 720.91 it/sec, obj=0.288]
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
INFO - 15:35:43: 22%|██▏ | 22/100 [00:00<00:00, 693.21 it/sec, obj=1.25]
INFO - 15:35:43: 23%|██▎ | 23/100 [00:00<00:00, 685.66 it/sec, obj=-0.875]
INFO - 15:35:43: 24%|██▍ | 24/100 [00:00<00:00, 699.88 it/sec, obj=1.01]
INFO - 15:35:43: 25%|██▌ | 25/100 [00:00<00:00, 700.49 it/sec, obj=-0.875]
INFO - 15:35:43: 26%|██▌ | 26/100 [00:00<00:00, 712.17 it/sec, obj=0.819]
INFO - 15:35:43: 27%|██▋ | 27/100 [00:00<00:00, 713.71 it/sec, obj=-0.875]
INFO - 15:35:43: 28%|██▊ | 28/100 [00:00<00:00, 725.12 it/sec, obj=0.693]
INFO - 15:35:43: 29%|██▉ | 29/100 [00:00<00:00, 720.21 it/sec, obj=0.584]
INFO - 15:35:43: 30%|███ | 30/100 [00:00<00:00, 720.77 it/sec, obj=-0.875]
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
INFO - 15:35:43: 31%|███ | 31/100 [00:00<00:00, 710.90 it/sec, obj=1.38]
INFO - 15:35:43: 32%|███▏ | 32/100 [00:00<00:00, 702.46 it/sec, obj=1.23]
INFO - 15:35:43: 33%|███▎ | 33/100 [00:00<00:00, 702.86 it/sec, obj=2.87]
INFO - 15:35:43: 34%|███▍ | 34/100 [00:00<00:00, 712.28 it/sec, obj=0.848]
INFO - 15:35:43: 35%|███▌ | 35/100 [00:00<00:00, 711.60 it/sec, obj=0.658]
INFO - 15:35:43: 36%|███▌ | 36/100 [00:00<00:00, 704.71 it/sec, obj=0.643]
INFO - 15:35:43: 37%|███▋ | 37/100 [00:00<00:00, 698.65 it/sec, obj=0.616]
INFO - 15:35:43: 38%|███▊ | 38/100 [00:00<00:00, 693.27 it/sec, obj=0.615]
INFO - 15:35:43: 39%|███▉ | 39/100 [00:00<00:00, 688.52 it/sec, obj=0.615]
INFO - 15:35:43: 40%|████ | 40/100 [00:00<00:00, 673.10 it/sec, obj=1.16]
INFO - 15:35:43: 41%|████ | 41/100 [00:00<00:00, 667.65 it/sec, obj=2.87]
INFO - 15:35:43: 42%|████▏ | 42/100 [00:00<00:00, 672.78 it/sec, obj=0.785]
INFO - 15:35:43: 43%|████▎ | 43/100 [00:00<00:00, 663.69 it/sec, obj=0.644]
INFO - 15:35:43: 44%|████▍ | 44/100 [00:00<00:00, 659.73 it/sec, obj=0.624]
INFO - 15:35:43: 45%|████▌ | 45/100 [00:00<00:00, 656.18 it/sec, obj=0.615]
INFO - 15:35:43: 46%|████▌ | 46/100 [00:00<00:00, 650.20 it/sec, obj=0.615]
INFO - 15:35:43: 47%|████▋ | 47/100 [00:00<00:00, 646.70 it/sec, obj=0.615]
INFO - 15:35:43: 48%|████▊ | 48/100 [00:00<00:00, 642.93 it/sec, obj=0.615]
INFO - 15:35:43: 49%|████▉ | 49/100 [00:00<00:00, 631.90 it/sec, obj=0.838]
INFO - 15:35:43: 50%|█████ | 50/100 [00:00<00:00, 624.87 it/sec, obj=0.656]
INFO - 15:35:43: 51%|█████ | 51/100 [00:00<00:00, 622.95 it/sec, obj=0.639]
INFO - 15:35:43: 52%|█████▏ | 52/100 [00:00<00:00, 620.49 it/sec, obj=0.616]
INFO - 15:35:43: 53%|█████▎ | 53/100 [00:00<00:00, 618.62 it/sec, obj=0.615]
INFO - 15:35:43: 54%|█████▍ | 54/100 [00:00<00:00, 616.66 it/sec, obj=0.615]
INFO - 15:35:43: 55%|█████▌ | 55/100 [00:00<00:00, 615.01 it/sec, obj=0.615]
INFO - 15:35:43: 56%|█████▌ | 56/100 [00:00<00:00, 613.34 it/sec, obj=0.615]
INFO - 15:35:43: 57%|█████▋ | 57/100 [00:00<00:00, 611.79 it/sec, obj=0.615]
INFO - 15:35:43: 58%|█████▊ | 58/100 [00:00<00:00, 607.70 it/sec, obj=0.625]
INFO - 15:35:43: 59%|█████▉ | 59/100 [00:00<00:00, 605.45 it/sec, obj=2.87]
INFO - 15:35:43: 60%|██████ | 60/100 [00:00<00:00, 609.47 it/sec, obj=0.616]
INFO - 15:35:43: 61%|██████ | 61/100 [00:00<00:00, 607.91 it/sec, obj=0.615]
INFO - 15:35:43: 62%|██████▏ | 62/100 [00:00<00:00, 606.24 it/sec, obj=0.615]
INFO - 15:35:43: 63%|██████▎ | 63/100 [00:00<00:00, 604.88 it/sec, obj=0.615]
INFO - 15:35:43: 64%|██████▍ | 64/100 [00:00<00:00, 603.88 it/sec, obj=0.615]
INFO - 15:35:43: 65%|██████▌ | 65/100 [00:00<00:00, 602.84 it/sec, obj=0.615]
INFO - 15:35:43: 66%|██████▌ | 66/100 [00:00<00:00, 604.85 it/sec, obj=0.615]
INFO - 15:35:43: 67%|██████▋ | 67/100 [00:00<00:00, 605.59 it/sec, obj=0.745]
INFO - 15:35:43: 68%|██████▊ | 68/100 [00:00<00:00, 603.25 it/sec, obj=-0.875]
INFO - 15:35:43: 69%|██████▉ | 69/100 [00:00<00:00, 603.43 it/sec, obj=-0.267]
INFO - 15:35:43: 70%|███████ | 70/100 [00:00<00:00, 605.15 it/sec, obj=-0.809]
INFO - 15:35:43: 71%|███████ | 71/100 [00:00<00:00, 609.56 it/sec, obj=-0.868]
INFO - 15:35:43: 72%|███████▏ | 72/100 [00:00<00:00, 613.95 it/sec, obj=-0.874]
INFO - 15:35:43: 73%|███████▎ | 73/100 [00:00<00:00, 615.46 it/sec, obj=-0.266]
INFO - 15:35:43: 74%|███████▍ | 74/100 [00:00<00:00, 616.84 it/sec, obj=0.135]
INFO - 15:35:43: 75%|███████▌ | 75/100 [00:00<00:00, 617.62 it/sec, obj=0.577]
INFO - 15:35:43: 76%|███████▌ | 76/100 [00:00<00:00, 621.67 it/sec, obj=0.288]
INFO - 15:35:43: 77%|███████▋ | 77/100 [00:00<00:00, 618.35 it/sec, obj=1.42]
INFO - 15:35:43: 78%|███████▊ | 78/100 [00:00<00:00, 617.74 it/sec, obj=-0.875]
INFO - 15:35:43: 79%|███████▉ | 79/100 [00:00<00:00, 619.36 it/sec, obj=-0.267]
INFO - 15:35:43: 80%|████████ | 80/100 [00:00<00:00, 623.11 it/sec, obj=-0.809]
INFO - 15:35:43: 81%|████████ | 81/100 [00:00<00:00, 627.11 it/sec, obj=-0.868]
INFO - 15:35:43: 82%|████████▏ | 82/100 [00:00<00:00, 630.98 it/sec, obj=-0.874]
INFO - 15:35:43: 83%|████████▎ | 83/100 [00:00<00:00, 632.14 it/sec, obj=-0.266]
INFO - 15:35:43: 84%|████████▍ | 84/100 [00:00<00:00, 633.15 it/sec, obj=0.135]
INFO - 15:35:43: 85%|████████▌ | 85/100 [00:00<00:00, 634.28 it/sec, obj=0.577]
INFO - 15:35:43: 86%|████████▌ | 86/100 [00:00<00:00, 638.07 it/sec, obj=0.288]
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
INFO - 15:35:43: 87%|████████▋ | 87/100 [00:00<00:00, 625.35 it/sec, obj=-0.267]
INFO - 15:35:43: 88%|████████▊ | 88/100 [00:00<00:00, 628.73 it/sec, obj=-0.809]
INFO - 15:35:43: 89%|████████▉ | 89/100 [00:00<00:00, 632.42 it/sec, obj=-0.868]
INFO - 15:35:43: 90%|█████████ | 90/100 [00:00<00:00, 635.98 it/sec, obj=-0.874]
INFO - 15:35:43: 91%|█████████ | 91/100 [00:00<00:00, 636.95 it/sec, obj=-0.266]
INFO - 15:35:43: 92%|█████████▏| 92/100 [00:00<00:00, 637.87 it/sec, obj=0.135]
INFO - 15:35:43: 93%|█████████▎| 93/100 [00:00<00:00, 638.82 it/sec, obj=0.577]
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 15:35:43: Optimization found no feasible point; the least infeasible point is selected.
INFO - 15:35:43: Exporting the optimization problem to the file multistart.hdf5
INFO - 15:35:43: Optimization result:
INFO - 15:35:43: Optimizer info:
INFO - 15:35:43: Status: None
INFO - 15:35:43: Message: None
INFO - 15:35:43: Number of calls to the objective function by the optimizer: 1
INFO - 15:35:43: Solution:
INFO - 15:35:43: The solution is feasible.
INFO - 15:35:43: Objective: 0.6150998205402495
INFO - 15:35:43: Standardized constraints:
INFO - 15:35:43: cstr = -0.7883188793606977
INFO - 15:35:43: Design space:
INFO - 15:35:43: +------+-------------+--------------------+-------------+-------+
INFO - 15:35:43: | Name | Lower bound | Value | Upper bound | Type |
INFO - 15:35:43: +------+-------------+--------------------+-------------+-------+
INFO - 15:35:43: | x | -1.5 | 0.5773502675245377 | 1.5 | float |
INFO - 15:35:43: +------+-------------+--------------------+-------------+-------+
INFO - 15:35:43: *** End MDOScenario execution (time: 0:00:00.165387) ***
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 0x7f52266ca930>
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 - 15:35:43: Importing the optimization problem from the file multistart.hdf5
<gemseo.post.basic_history.BasicHistory object at 0x7f52266cb380>
Total running time of the script: (0 minutes 0.545 seconds)