Version: 0.6.1.3

# SYM-PART¶

The SYM-PART [51] 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()

[1]:

<pymoo.visualization.scatter.Scatter at 0x111485d30>


### Pareto front¶

[2]:

pf = problem.pareto_front()

[2]:

<pymoo.visualization.scatter.Scatter at 0x127a95190>


## 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()

[3]:

<pymoo.visualization.scatter.Scatter at 0x127c23e90>


### Pareto front¶

[4]:

pf = problem.pareto_front()

[4]:

<pymoo.visualization.scatter.Scatter at 0x127c7bbf0>