New Tunable Test Problems for Benchmarking Niching Methods for Multimodal Optimization

Genetic and Evolutionary Computation Conference (GECCO), pp. 4–12

Abstract

This study introduces novel tunable benchmark test problems for continuous box-constrained multimodal optimization (MMO). It first introduces a new approach to control the non-uniformity of distribution of global minima, a notable challenge in MMO. Then, it builds upon an existing procedure to create composite functions in which the severity of two distinguishable groups of MMO challenges can be controlled: i) challenges shared with global optimization (GO), such as ill-conditioning, and ii) challenges specific to MMO, such as non-uniform distribution of global minima. Eight new scalable and tunable MMO functions are then proposed, based on which a test suite of 16 continuous MMO test problems is suggested. This test suite is designed to be i) comprehensive, which means they simulate most, if not all, prominent challenges associated with MMO, ii) discriminating, which means test problems can disclose the gap between the performance of diverse MMO methods, and iii) illuminating, which means test problems can reveal and compare strengths and weaknesses of MMO methods. The code of these problems is made available in two different programming languages to encourage its adoption by the research community.

Authors 5

1. Ali Ahrari

   UNSW Canberra

   Affiliation as printed

   The University of New South Wales, Canberra, Australia

2. Jonathan Edward Fieldsend

   University of Exeter

   Affiliation as printed

   University of Exeter, Exeter, United Kingdom

3. Mike Preuß Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Leiden, Netherlands

4. Xiaodong Li

   RMIT University

   Affiliation as printed

   RMIT University, Melbourne, Australia

5. Michael G. Epitropakis
   Affiliation as printed

   The Signal Group, Glyfada, Greece