Note
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Pareto front on Binh and Korn problem¶
In this example, we illustrate the use of the ParetoFront plot
on the Binh and Korn multi-objective problem.
from __future__ import annotations
from gemseo.algos.doe.doe_factory import DOEFactory
from gemseo.api import configure_logger
from gemseo.post.post_factory import PostFactory
from gemseo.problems.analytical.binh_korn import BinhKorn
Import¶
The first step is to import some functions from the API and a method to get the design space.
configure_logger()
<RootLogger root (INFO)>
Import the optimization problem¶
Then, we instantiate the BinkKorn optimization problem.
problem = BinhKorn()
Create and execute scenario¶
Then, we create a Design of Experiment factory, and we request the execution a a full-factorial DOE using 100 samples
doe_factory = DOEFactory()
doe_factory.execute(problem, algo_name="OT_OPT_LHS", n_samples=100)
INFO - 16:55:30: Optimization problem:
INFO - 16:55:30: minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
INFO - 16:55:30: with respect to x, y
INFO - 16:55:30: subject to constraints:
INFO - 16:55:30: ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
INFO - 16:55:30: ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
INFO - 16:55:30: over the design space:
INFO - 16:55:30: +------+-------------+-------+-------------+-------+
INFO - 16:55:30: | name | lower_bound | value | upper_bound | type |
INFO - 16:55:30: +------+-------------+-------+-------------+-------+
INFO - 16:55:30: | x | 0 | 1 | 5 | float |
INFO - 16:55:30: | y | 0 | 1 | 3 | float |
INFO - 16:55:30: +------+-------------+-------+-------------+-------+
INFO - 16:55:30: Solving optimization problem with algorithm OT_OPT_LHS:
INFO - 16:55:30: ... 0%| | 0/100 [00:00<?, ?it]
INFO - 16:55:30: ... 1%| | 1/100 [00:00<00:00, 3127.74 it/sec, obj=[98.50728236 17.96432773]]
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INFO - 16:55:31: ... 95%|█████████▌| 95/100 [00:00<00:00, 1942.30 it/sec, obj=[17.335399 26.84155459]]
INFO - 16:55:31: ... 96%|█████████▌| 96/100 [00:00<00:00, 1943.79 it/sec, obj=[ 4.93473731 35.93049995]]
INFO - 16:55:31: ... 97%|█████████▋| 97/100 [00:00<00:00, 1945.21 it/sec, obj=[25.16386975 26.89754332]]
INFO - 16:55:31: ... 98%|█████████▊| 98/100 [00:00<00:00, 1946.61 it/sec, obj=[81.61206359 10.43246637]]
INFO - 16:55:31: ... 99%|█████████▉| 99/100 [00:00<00:00, 1944.71 it/sec, obj=[40.83406128 15.59204339]]
INFO - 16:55:31: ... 100%|██████████| 100/100 [00:00<00:00, 1942.77 it/sec, obj=[52.02690192 12.02601654]]
INFO - 16:55:31: Optimization result:
INFO - 16:55:31: Optimizer info:
INFO - 16:55:31: Status: None
INFO - 16:55:31: Message: None
INFO - 16:55:31: Number of calls to the objective function by the optimizer: 100
INFO - 16:55:31: Solution:
INFO - 16:55:31: The solution is feasible.
INFO - 16:55:31: Objective: 30.39964825035985
INFO - 16:55:31: Standardized constraints:
INFO - 16:55:31: ineq1 = [-11.77907222]
INFO - 16:55:31: ineq2 = [-38.26307397]
INFO - 16:55:31: Design space:
INFO - 16:55:31: +------+-------------+-------------------+-------------+-------+
INFO - 16:55:31: | name | lower_bound | value | upper_bound | type |
INFO - 16:55:31: +------+-------------+-------------------+-------------+-------+
INFO - 16:55:31: | x | 0 | 1.542975634014225 | 5 | float |
INFO - 16:55:31: | y | 0 | 1.269910308585573 | 3 | float |
INFO - 16:55:31: +------+-------------+-------------------+-------------+-------+
Optimization result:
Design variables: [1.54297563 1.26991031]
Objective function: 30.39964825035985
Feasible solution: True
Post-process scenario¶
Lastly, we post-process the scenario by means of the ParetoFront
plot which generates a plot or a matrix of plots if there are more than
2 objectives, plots in blue the locally non dominated points for the current
two objectives, plots in green the globally (all objectives) Pareto optimal
points. The plots in green denotes non-feasible points. Note that the user
can avoid the display of the non-feasible points.
PostFactory().execute(
problem,
"ParetoFront",
show_non_feasible=False,
objectives=["compute_binhkorn"],
objectives_labels=["f1", "f2"],
save=False,
show=True,
)
PostFactory().execute(
problem,
"ParetoFront",
show_non_feasible=True,
objectives=["compute_binhkorn"],
objectives_labels=["f1", "f2"],
save=False,
show=True,
)
<gemseo.post.pareto_front.ParetoFront object at 0x7fbc55732f40>
Total running time of the script: ( 0 minutes 0.457 seconds)