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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 import configure_logger
from gemseo.algos.doe.doe_factory import DOEFactory
from gemseo.post.post_factory import PostFactory
from gemseo.problems.analytical.binh_korn import BinhKorn
Import¶
The first step is to import a high-level function for logging.
configure_logger()
<RootLogger root (INFO)>
Import the optimization problem¶
Then, we instantiate the Binh and Korn optimization problem (see BinhKorn).
problem = BinhKorn()
Create and execute scenario¶
Then, we instantiate the design of experiment factory, and we request the execution of a 100-length LHS optimized by simulated annealing.
doe_factory = DOEFactory()
doe_factory.execute(problem, algo_name="OT_OPT_LHS", n_samples=100)
INFO - 10:57:47: Optimization problem:
INFO - 10:57:47: minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
INFO - 10:57:47: with respect to x, y
INFO - 10:57:47: subject to constraints:
INFO - 10:57:47: ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
INFO - 10:57:47: ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
INFO - 10:57:47: over the design space:
INFO - 10:57:47: +------+-------------+-------+-------------+-------+
INFO - 10:57:47: | Name | Lower bound | Value | Upper bound | Type |
INFO - 10:57:47: +------+-------------+-------+-------------+-------+
INFO - 10:57:47: | x | 0 | 1 | 5 | float |
INFO - 10:57:47: | y | 0 | 1 | 3 | float |
INFO - 10:57:47: +------+-------------+-------+-------------+-------+
INFO - 10:57:47: Solving optimization problem with algorithm OT_OPT_LHS:
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INFO - 10:57:47: Optimization result:
INFO - 10:57:47: Optimizer info:
INFO - 10:57:47: Status: None
INFO - 10:57:47: Message: None
INFO - 10:57:47: Number of calls to the objective function by the optimizer: 100
INFO - 10:57:47: Solution:
INFO - 10:57:47: The solution is feasible.
INFO - 10:57:47: Objective: 30.39964825035985
INFO - 10:57:47: Standardized constraints:
INFO - 10:57:47: ineq1 = [-11.77907222]
INFO - 10:57:47: ineq2 = [-38.26307397]
INFO - 10:57:47: Design space:
INFO - 10:57:47: +------+-------------+-------------------+-------------+-------+
INFO - 10:57:47: | Name | Lower bound | Value | Upper bound | Type |
INFO - 10:57:47: +------+-------------+-------------------+-------------+-------+
INFO - 10:57:47: | x | 0 | 1.542975634014225 | 5 | float |
INFO - 10:57:47: | y | 0 | 1.269910308585573 | 3 | float |
INFO - 10:57:47: +------+-------------+-------------------+-------------+-------+
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 denote 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",
objectives=["compute_binhkorn"],
objectives_labels=["f1", "f2"],
save=False,
show=True,
)
<gemseo.post.pareto_front.ParetoFront object at 0x7efd268a1e20>
Total running time of the script: (0 minutes 0.505 seconds)