An ensemble approach with external archive for multi- and many-objective optimization with adaptive mating mechanism and two-level environmental selection

Abstract

Based on mating and environmental selections employed, multi-objective evolutionary algorithms (MOEAs) are classified as Pareto-based, decomposition-based and indicator-based approaches that are associated with their own advantages and disadvantages. To benefit from the advantages of different MOEAs, we propose an ensemble framework (ENMOEA) in which mating and environmental selections of diverse MOEAs are combined. ENMOEA is a single-population competitive ensemble, where resource allocation to individual mating operators is done adaptively. In addition, ENMOEA employs a two-level environmental selection where constituent environmental selection operators are first applied to label solutions as “selected” and “non-selected”. Solutions “selected” by most operators are preferred for future evolution. An external archive is employed to facilitate effective usage of function evaluations and achieve a better comprise between convergence and diversity. To demonstrate generality of ENMOEA, we developed two variants: 1) specific case (ENMOEAS - combines different Pareto-based MOEAs) and 2) general case (ENMOEAG - combines Pareto-based, indicator-based and decomposition-based MOEAs). From simulation results on various test suites (DTLZ, WFG and 16 real-world problems), it is evident that ENMOEA is robust to the parameters of the constituent algorithms. In addition, it is evident that the effectiveness of ensemble improves with the diversity of the constituent algorithms.