A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions

Abstract

A knee region on the Pareto-optimal front of a multi-objective optimization problem consists of solutions with the maximum marginal rates of return, i.e. solutions for which an improvement on one objective is accompanied by a severe degradation in another. The trade-off characteristic renders such solutions of particular interest in practical applications. This paper presents a multi-objective evolutionary algorithm focused on the knee regions. The algorithm facilitates better decision making in contexts where high marginal rates of return are desirable for Decision Makers. The proposed approach computes a transformation of the original objectives based on weighted-sum functions. The transformed functions identify niches which correspond to knee regions in the objective space. The extent and density of coverage of the knee regions are controllable by the niche strength and pool size parameters. Although based on weighted-sums, the algorithm is capable of finding solutions in the non-convex regions of the Pareto-front.