Benchmarking Modern Evolutionary Algorithms for Multi-Modal Multi-Objective Optimization: A Comprehensive Performance Matrix Analysis

Abstract

The multi-modal multi-objective optimization (MMO) paradigm has received greater attention because of its applicability and affinity for mapping problems. Multi-objective problems can be solved by classical evolutionary algorithms, also known as EAs, as they are the ideal candidates for solving these complex problems. However, these EAs are deficient in addressing issues related to multi-modal functions. Likewise, modern EAs have been shown to solve various benchmark functions and optimization problems. But the extent of analyzing its performance comprehensively on today’s complex EAs is remarkably scarce in the literature regarding the proposal of the MMO function. This study conducts an extensive analysis of modern EAs on benchmark MMO functions (six functions and three EA algorithms). These include spacing, spread, distance, diversity, convergence, and the run-time identified properties. The properties are then linked with the twelve performance metrics. This work also introduced the optimal EA for managing the MMO benchmark function. The empirical evidence used in the proposed framework is the performance matrix to select the best EA for the function of MMO.