Software for Generation of Classes of Test Functions with Known Local and Global Minima for Global Optimization

TL;DR

This paper introduces a method and software package for generating diverse classes of test functions with known minima, aiding the evaluation of global optimization algorithms.

Contribution

It presents a systematic procedure and C routines for creating test functions with controlled local and global minima, including non-differentiable and differentiable classes.

Findings

Generated 100 functions per class with known minima

Provided full details of minima and derivatives where possible

Enabled customizable test functions for optimization benchmarking

Abstract

A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization and a corresponding package of C subroutines are presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.