Multi-objective particle swarm optimization by fuzzy-pareto-dominance meta-heuristic

Abstract

This paper introduces a new approach to multi-objective Particle Swarm Optimization (PSO). The approach is based on the recently proposed Fuzzy-Pareto-Dominance (FPD) relation. FPD is a generic ranking scheme, where ranking values are mapped to element vectors of a set. These ranking values are directly computed from the element vectors of the set and can be used to perform rank operations (e.g. selecting the “largest”) with the vectors within the given set. FPD can be seen as a paradigm or meta-heuristic to formally expand single-objective optimization algorithms to multi-objective optimization algorithms, as long as such vector-sets can be defined. This was already shown for the Standard Genetic Algorithm. Here, we explore the application of this concept to PSO, where a swarm of particles is maintained. The resulting ${\mathrm{PSO}}_{\mathit{f}2\mathit{r}}$ algorithm is studied on a fundamental optimization problem (so-called Pareto-Box-Problem) where a complete analysis is possible. The ${\mathrm{PSO}}_{\mathit{f}2\mathit{r}}$ algorithm is shown to handle the case of a larger number of objectives, and shows similar properties like the (single-objective) PSO.