Comparing the Performance of Evolutionary Algorithms for Sparse Multi-Objective Optimization via a Comprehensive Indicator [Research Frontier

Abstract

Many real-world multi-objective optimization problems (MOPs) are characterized by a large number of decision variables, where the decision variables are mostly set to zero in the Pareto optimal solutions. Although some multi-objective evolutionary algorithms (MOEAs) have been tailored for large-scale MOPs in recent years, most of them do not consider the sparse nature of Pareto optimal solutions, and their effectiveness to sparse MOPs has not been investigated. Therefore, this work aims to compare the performance of MOEAs on sparse MOPs by suggesting a comprehensive performance indicator. In comparison to existing indicators assessing the convergence and diversity of a solution set according to predefined reference points, the proposed indicator can assess the convergence, diversity, and sparsity without using any reference point. Based on the proposed indicator, an experiment is conducted to compare the performance of 11 state-of-the-art MOEAs on 60 test instances taken from benchmark suites and real-world applications. The statistical results show that some MOEAs are significantly better than the others for solving sparse MOPs, and the proposed indicator is effective for the performance assessment on sparse MOPs.