Decomposition Based Evolutionary Algorithm with a Dual Set of reference vectors

Abstract

Decomposition based approaches are increasingly being used to solve many-objective optimization problems (MaOPs). In such approaches, the MaOP is decomposed into several single-objective sub-problems and solved simultaneously guided by a set of predefined, uniformly distributed reference vectors. The reference vectors are constructed by joining a set of uniformly sampled points to the ideal point. Use of such reference vectors originating from the ideal point has so far performed reasonably well on common benchmarks such as DTLZs and WFGs, since the geometry of their Pareto fronts can be easily mapped using these reference vectors. However, the approach may not deliver a set of well distributed solutions for problems with Pareto fronts which are convex/concave or where the shape of the Pareto front is not best suited for such set of reference vectors (e.g. minus series of DTLZ and WFG test problems). While the notion of reference vectors originating from the nadir point has been suggested in the literature in the past, they have rarely been used in decomposition based algorithms. Such reference vectors are complementary in nature with the ones originating from the ideal point. Therefore, in this paper, we introduce a decomposition based approach which attempts to use both these two sets of reference vectors and chooses the most appropriate set at each generation based on the s-energy metric. The performance of the approach is presented and objectively compared with a number of recent algorithms. The results clearly highlight the benefits of such an approach especially when the nature of the Pareto front is not known a priori.