pymoo
Latest Version: pymoo==0.4.1

ZakharovΒΆ

The Zakharov function has no local minima except the global one. It is shown here in its two-dimensional form.

Definition

\begin{align} \begin{split} f(x) &=& \sum\limits_{i=1}^n {x_i^2} + \bigg( \frac{1}{2} \sum\limits_{i=1}^n {ix_i} \bigg)^2 + \bigg( \frac{1}{2} \sum\limits_{i=1}^n {ix_i} \bigg)^4, \\[2mm] && -10 \leq x_i \leq 10 \quad i=1,\ldots,n \end{split} \end{align}

Optimum

\[f(x^*) = 0 \; \text{at} \; x^* = (0,\ldots,0)\]

Contour

[1]:
import numpy as np
from pymoo.factory import get_problem, get_visualization

problem = get_problem("zakharov", n_var=2)
get_visualization("fitness-landscape", problem, angle=(45, 45), _type="surface").show()
get_visualization("fitness-landscape", problem, _type="contour", contour_levels = 200, colorbar=True).show()
../../_images/problems_single_zakharov_7_0.png
../../_images/problems_single_zakharov_7_1.png
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