An improved multi-objective population-based extremal optimization algorithm with polynomial mutation

As a recently developed evolutionary algorithm inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of benchmark and engineering optimization problems. However, there are only few reported research works concerning the applications of EO in the field of multi-objective optimization. This paper presents an improved multi-objective population-based EO algorithm with polynomial mutation called IMOPEO-PLM to solve multi-objective optimization problems (MOPs). Unlike the previous multi-objective versions based on EO, the proposed IMOPEO-PLM adopts population-based iterated optimization, a more effective mutation operation called polynomial mutation, and a novel and more effective mechanism of generating new population. From the design perspective of multi-objective evolutionary algorithms (MOEAs), IMOPEO-PLM is relatively simpler than other reported competitive MOEAs due to its fewer adjustable parameters and only mutation operation. Furthermore, the extensive experimental results on some benchmark MOPs show that IMOPEO-PLM performs better than or at least competitive with these reported popular MOEAs, such as MOPEO, MOEO, NSGA-II, A-MOCLPSO, PAES, SPEA, SPEA2, SMS-EMOA, SMPSO, and MOEA/D-DE, by using nonparametric statistical tests, e.g., Kruskal–Wallis test, Mann–Whitney U test, Friedman and Quade tests, in terms of some commonly-used quantitative performance metrics, e.g., convergence, diversity (spread), hypervolume, generational distance, inverted generational distance.