Fusion of many-objective non-dominated solutions using reference points

Abstract

With recent advancements of multi- or many-objective optimization algorithms, researchers and decision-makers are increasingly faced with the dilemma of choosing the best algorithm to solve their problems. In this paper, we propose a simple hybridization of population-based multi- or many-objective optimization algorithms called fusion of non-dominated fronts using reference points (FNFR) to gain combined benefits of several algorithms. FNFR combines solutions from multiple optimization algorithms during or after several runs and extracts well-distributed solutions from a large set of non-dominated solutions using predefined structured reference points or user-defined reference points. The proposed FNFR is applied to non-dominated solutions obtained by the Generalized Differential Evolution Generation 3 (GDE3), Speed-constrained Multi-objective Particle Swarm Optimization (SMPSO), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2) on seven unconstrained many-objective test problems with three to ten objectives. Experimental results show FNFR is an effective way for combining and extracting (fusion) of well-distributed non-dominated solutions among a large set of solutions. In fact, the proposed method is a solution-level hybridization approach. FNFR showed promising results when selecting well-distributed solutions around a specific region of interest.