Investigation of a Simple Distance Based Ranking Metric for Decomposition-Based Multi/Many-Objective Evolutionary Algorithms

Abstract

Multi-objective problems with more than three objectives, more commonly referred to as many-objective problems, have lately been a subject of significant research interest. Decomposition of the objective space is one of the most widely used approaches, where the original problem is decomposed into several single-objective sub-problems and solved collaboratively. The sub-problems are defined using reference vectors, to which candidate solutions are assigned based on some proximity measures (e.g. perpendicular distance/angle etc.). The individuals attached to a given reference vector can thus be considered as a sub-population trying to solve that sub-problem. To create selection pressure among the members of the sub-population, several measures have been proposed in the past; such as weighted sum, penalty boundary intersection, achievement scalarizing function, Tchebycheff, etc. While being competitive, some of them require parameters or reference points for implementation, which is far from ideal. The aim of this study is to investigate an alternative, less explored avenue - the use of distance based ranking with a decomposition based algorithm. Towards this end, we propose an improved version of an existing distance based metric and embed it within a decomposition based evolutionary algorithm (DBEA-MDR). We characterize its performance through a comprehensive benchmarking on a range of regular and inverted DTLZ/WFG problems. While the performance of DBEA-MDR based on conventional benchmarking practice (quality of solutions of the final populations) is not competitive with existing state-of-the-art algorithms, selection of a diverse set of solutions (of same size as the population) from the archive significantly improves its performance which in a number of cases supersedes the performance of other algorithms. Based on these observations, apart from highlighting the scope of improvement in the presented strategy, the study also emphasizes the need to look into existing benchmarking practices further. In particular, instead of the performance judged by the final population, a better approximation set could be found from the archive and performance judged on such sets would be more reflective of the true performance of the algorithms.