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 import configure_logger
from gemseo.algos.doe.factory import DOELibraryFactory
from gemseo.post.factory import PostFactory
from gemseo.problems.multiobjective_optimization.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 = DOELibraryFactory()
doe_factory.execute(problem, algo_name="OT_OPT_LHS", n_samples=100)

INFO - 08:38:48: Optimization problem:
INFO - 08:38:48:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
INFO - 08:38:48:    with respect to x, y
INFO - 08:38:48:    subject to constraints:
INFO - 08:38:48:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
INFO - 08:38:48:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
INFO - 08:38:48:    over the design space:
INFO - 08:38:48:       +------+-------------+-------+-------------+-------+
INFO - 08:38:48:       | Name | Lower bound | Value | Upper bound | Type  |
INFO - 08:38:48:       +------+-------------+-------+-------------+-------+
INFO - 08:38:48:       | x    |      0      |   1   |      5      | float |
INFO - 08:38:48:       | y    |      0      |   1   |      3      | float |
INFO - 08:38:48:       +------+-------------+-------+-------------+-------+
INFO - 08:38:48: Solving optimization problem with algorithm OT_OPT_LHS:
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INFO - 08:38:48:     98%|█████████▊| 98/100 [00:00<00:00, 2399.98 it/sec, obj=[81.61206359 10.43246637]]
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INFO - 08:38:48:    100%|██████████| 100/100 [00:00<00:00, 2400.75 it/sec, obj=[52.02690192 12.02601654]]
INFO - 08:38:48: Optimization result:
INFO - 08:38:48:    Optimizer info:
INFO - 08:38:48:       Status: None
INFO - 08:38:48:       Message: None
INFO - 08:38:48:       Number of calls to the objective function by the optimizer: 100
INFO - 08:38:48:    Solution:
INFO - 08:38:48:       The solution is feasible.
INFO - 08:38:48:       Objective: 30.39964825035985
INFO - 08:38:48:       Standardized constraints:
INFO - 08:38:48:          ineq1 = [-11.77907222]
INFO - 08:38:48:          ineq2 = [-38.26307397]
INFO - 08:38:48:       Design space:
INFO - 08:38:48:          +------+-------------+-------------------+-------------+-------+
INFO - 08:38:48:          | Name | Lower bound |       Value       | Upper bound | Type  |
INFO - 08:38:48:          +------+-------------+-------------------+-------------+-------+
INFO - 08:38:48:          | x    |      0      | 1.542975634014225 |      5      | float |
INFO - 08:38:48:          | y    |      0      | 1.269910308585573 |      3      | float |
INFO - 08:38:48:          +------+-------------+-------------------+-------------+-------+
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 denote non-feasible points. Note that the user can avoid the display of the non-feasible points.

PostFactory().execute(
    problem,
    post_name="ParetoFront",
    show_non_feasible=False,
    objectives=["compute_binhkorn"],
    objectives_labels=["f1", "f2"],
    save=False,
    show=True,
)

PostFactory().execute(
    problem,
    post_name="ParetoFront",
    objectives=["compute_binhkorn"],
    objectives_labels=["f1", "f2"],
    save=False,
    show=True,
)
  • Pareto front
  • Pareto front
<gemseo.post.pareto_front.ParetoFront object at 0x7f6dc8172490>

Total running time of the script: (0 minutes 0.553 seconds)

Download Jupyter notebook: plot_pareto_front_binhkorn.ipynb

Download Python source code: plot_pareto_front_binhkorn.py

Download zipped: plot_pareto_front_binhkorn.zip

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