SYM-PART¶

The SYM-PART [34] problem suite is a multi-modal multi-objective optimization problem (MMOP). In MMOPs, a solution :math:y in the objective space may have several inverse images in the decision space. For this reason, an MMOP could have more than one Pareto subsets.

The SYM-PART has two variants: SYM-PART simple and SYM-PART rotated. Both of them have the same Pareto front. But their Pareto sets are different.

1. SYM-PART Simple¶

Pareto subsets¶

[1]:

from pymoo.problems.multi.sympart import SYMPART, SYMPARTRotated
from pymoo.visualization.scatter import Scatter

problem = SYMPART()
ps = problem.pareto_set()
Scatter(title="Pareto set", xlabel="$x_1$", ylabel="$x_2$").add(ps).show()


Pareto front¶

[2]:

pf = problem.pareto_front()


2. SYM-PART Rotated¶

Pareto subsets¶

The pareto subsets can be rotated.

[3]:

from numpy import pi

# rotate pi/3 counter-clockwisely
problem = SYMPARTRotated(angle=pi/3)
ps = problem.pareto_set()
Scatter(title="Pareto set", xlabel="$x_1$", ylabel="$x_2$").add(ps).show()


Pareto front¶

[4]:

pf = problem.pareto_front()