An investigation of clustering strategies in many-objective optimization: the I-Multi algorithm as a case study

Abstract

A variety of general strategies have been applied to enhance the performance of multi-objective optimization algorithms for many-objective optimization problems (those with more than three objectives). One of these strategies is to split the solutions to cover di↵erent regions (clusters) and apply an optimizer to each region with the aim of producing more diverse solutions and achieving a better distributed approximation of the Pareto front. However, the e↵ectiveness of clustering in this context depends on a number of issues, including the characteristics of the objective functions. In this paper we show how the choice of the clustering strategy can greatly influence the behavior an optimizer. We try to find a relation between the characteristics a of multi-objective optimization problem (MOP) and the e ciency of the use of a clustering type in its resolution. Using as a case study, the Iterated Multi-swarm (I-Multi), a recently introduced multi-objective particle swarm optimization (MOPSO) algorithm, we scrutinize the impact that clustering in di↵erent spaces (of variables, objectives, and a combination of both) can have on the approximations of the Pareto front. Furthermore, using two difficult function benchmarks of problems of up to 20 objectives, we evaluate the e↵ect of using di↵erent metrics for determining the similarity between the solutions during the clustering process. Our results confirm the important e↵ect of the clustering strategy on the behavior of multi-objective optimizers. Moreover, we present evidence that some problem characteristics can be used to select the most e↵ective clustering strategy, significantly improving the quality of the Pareto front approximations produced by I-Multi.

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