Constrained many-objective optimization: a way forward

Abstract

Many objective optimization is a natural extension to multi-objective optimization where the number of objectives are significantly more than five. The performance of current state of the art algorithms (e.g. NSGA-II, SPEA2) is known to deteriorate significantly with increasing number of objectives due to the lack of adequate convergence pressure. It is of no surprise that the performance of NSGA-II on some constrained many-objective optimization problems (Deb and Saxena, 2006) (e.g., DTLZ5-(5,M), M = 10, 20) in an earlier study (Saxena, 2008) was far from satisfactory. Till date, research in many-objective optimization has focussed on two major areas (a) dimensionality reduction in the objective space and (b) preference ordering based approaches. This paper introduces a novel evolutionary algorithm powered by epsilon dominance (implemented within the framework of NSGA-II) and controlled infeasibility for improved convergence while the critical set of objectives is identified through a nonlinear dimensionality reduction scheme. Since approaching the Pareto-optimal front from within the feasible search space will need to overcome the problems associated with low selection pressure, the mechanism to approach the front from within the infeasible search space is promising as illustrated in this paper. The performance of the proposed algorithm is compared with NSGA-II (original, with crowding distance measure) and NSGA-II (epsilon dominance) on the above set of constrained multiobjective problems to highlight the benefits.