Global optimization test problems based on random field composition

TL;DR

This paper introduces a systematic method to generate complex, tunable global optimization test problems using weighted composition of random fields, aiding in the evaluation of optimization algorithms.

Contribution

It presents a novel approach to create customizable test functions with controllable difficulty features for better algorithm assessment.

Findings

Method enables construction of challenging test functions with tunable features.

Applicable to performance analysis of optimization algorithms.

Provides a MATLAB implementation for practical use.

Abstract

The development and identification of effective optimization algorithms for non-convex real-world problems is a challenge in global optimization. Because theoretical performance analysis is difficult, and problems based on models of real-world systems are often computationally expensive, several artificial performance test problems and test function generators have been proposed for empirical comparative assessment and analysis of metaheuristic optimization algorithms. These test problems however often lack the complex function structures and forthcoming difficulties that can appear in real-world problems. This communication presents a method to systematically build test problems with various types and degrees of difficulty. By weighted composition of parameterized random fields, challenging test functions with tunable function features such as, variance contribution distribution, interaction order, and nonlinearity can be constructed. The method is described, and its applicability to optimization performance analysis is described by means of a few basic examples. The method aims to set a step forward in the systematic generation of global optimization test problems, which could lead to a better understanding of the performance of optimization algorithms on problem types with particular characteristics. On request an introductive MATLAB implementation of a test function generator based on the presented method is available.