Mathematical Definition

\[f(\mathbf x)=f(x_1, ..., x_n)=\sum_{i=1}^n |x_i|\]

Plots

Contour of the function is presented below:

Description and Features

• The function is continuous.
• The function is convex.
• The function is defined on n-dimensional space.
• The function is unimodal.
• The function is non-differentiable.
• The function is separable.

Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-100, 100]$ for $i=1, …, n$.

Global Minima

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

Implementation

Python

For Python, the function is implemented in the benchmarkfcns package, which can be installed from command line with pip install benchmarkfcns.

from benchmarkfcns import schwefel220

print(schwefel220([[0, 0, 0],
              [1, 1, 1]]))

MATLAB

An implementation of the Schwefel 2.20 Function with MATLAB is provided below.

% Computes the value of the Schwefel 2.20 function.
% SCORES = SCHWEFEL220FCN(X) computes the value of the Schwefel 2.20 
% function at point X. SCHWEFEL220FCN accepts a matrix of size M-by-N and 
% returns a vetor SCORES of size M-by-1 in which each row contains the 
% function value for the corresponding row of X.
% 
% Author: Mazhar Ansari Ardeh
% Please forward any comments or bug reports to mazhar.ansari.ardeh at
% Google's e-mail service or feel free to kindly modify the repository.
function scores = schwefel220fcn(x)
    scores = sum(abs(x), 2);
end

The function can be represented in Latex as follows:

f(\mathbf x)=f(x_1, ..., x_n)=\sum_{i=1}^n |x_i|

References:

• Momin Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation}, Vol. 4, No. 2, pp. 150–194 (2013), arXiv:1308.4008
• H. P. Schwefel, “Numerical Optimization for Computer Models,” John Wiley Sons, 1981.