An enhancing many-objective evolutionary algorithm using chaotic mapping and solution ranking mechanism for large-scale optimization

Abstract

Abstract There are many complex optimization problems in the real world, and various evolutionary algorithms are proposed to solve them. Recently, the many-objective evolutionary algorithm using a one-by-one selection strategy (1by1EA) adopts a convergence indicator and a distribution indicator to balance convergence and diversity. However, the algorithm is too random in initialization and the fitness evaluation of solutions in the mating selection is single, which leads to poor performance in solving large-scale problems. Therefore, this paper proposes an improved method called 1by1EA-CHV by using circle chaotic mapping and a solution ranking mechanism based on the hypervolume (HV) indicator. We first map each component of solutions into a certain value space to initialize the population. Then, we calculate the contribution of each partition divided based on HV and apply the aggregation method to guide the reallocation of fitness, which achieves the ranking of solutions by using it before the old calculation method. To validate the performance, experiments compared 1by1EA-CHV with 1by1EA and other seven many-objective algorithms on large-scale functions, and the differences between these algorithms were analyzed statistically by a non-parametric test. The results showed the superiority of 1by1EA-CHV in solving large-scale many-objective optimization problems with up to 2000 decision variables.