Plots

Two contours of the function are presented below:

Description and Features

• The function is continuous.
• The function is not convex.
• The function is defined on n-dimensional space.
• The function is multimodal.
• The function is differentiable.
• The function is non-separable.

Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-10, 10]$ for $i=1, …, n$.

Global Minima

The function has 18 global minima $f(\textbf{x}^{\ast})\approx-186.7309$.

Implementation

An implementation of the Shubert Function with MATLAB is provided below.

The function can be represented in Latex as follows:

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
• E. P. Adorio, U. P. Dilman, “MVF - Multivariate Test Function Library in C for Unconstrained Global Optimization Methods,” [Available Online]: http://www.geocities.ws/eadorio/mvf.pdf