Schwefel

Mathematical Definition
Latex
f(x) = {418.9829d -{\sum_{i=1}^{n} x_i sin(\sqrt{|x_i|})}}
Description and Features

Dimensions: d

The Schwefel function is complex, with many local minima. The plot shows the two-dimensional form of the function.

  • The function is continuous.
  • The function is convex.
  • The function is defined on n-dimensional space.
  • The function is multimodal.
Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-500, 500]$ for $i = 1, …, d$ .

Global Minima

The function has one global minimum $f(\textbf{x}^{\ast})=0$ at $\textbf{x}^{\ast} = (420.9687, …, 420.9687)$.

Implementation
Python Code

def function(x):
    x = np.array(x)
    alpha = 418.9829
    return alpha * len(x) - (x * np.sin(np.sqrt(np.abs(x)))).sum()

            
Solutions
References: