Version: 0.5.0

# Omni-test¶

The Omni-test problem is a multi-modal multi-objective optimization problem proposed by Deb in [40]. It has two objective functions. Suppose that the dimension of the decision space is $$D$$, then it has $$3^D$$ Pareto subsets in the decision space corresponding to the same Pareto front.

## 2-dimensional case¶

### Pareto front¶

[1]:

from pymoo.problems.multi.omnitest import OmniTest
from pymoo.visualization.scatter import Scatter

problem = OmniTest(n_var=2)
pf = problem.pareto_front(1000)

[1]:

<pymoo.visualization.scatter.Scatter at 0x7f5561b4f9a0>


### Pareto set¶

[2]:

ps = problem.pareto_set(1000)
Scatter(title="Pareto set", labels=["$x_1$", "$x_2$"]).add(ps).show()

[2]:

<pymoo.visualization.scatter.Scatter at 0x7f5561b4fb80>


## 3-dimensional case¶

### Pareto front¶

[3]:

problem = OmniTest(n_var=3)
pf = problem.pareto_front(3000)

[3]:

<pymoo.visualization.scatter.Scatter at 0x7f5552915670>


### Pareto set¶

[4]:

import matplotlib.pyplot as plt

ps = problem.pareto_set(1000)
sc = Scatter(title="Pareto set", labels=["$x_1$", "$x_2$", "$x_3$"])