A multi-objective particle swarm optimizer based on reference point for multimodal multi-objective optimization

Abstract

In real-world applications, there are many multimodal multi-objective optimization problems, which have multiple equivalent global Pareto-optimal solutions or with at least one local Pareto-optimal solution in the decision space. While some evolutionary algorithms have been proposed to find the global solutions recently, they are difficult to handle multimodal multi-objective optimization problems with local solutions. Meanwhile, there have been few studies on searching for local Pareto solutions. However, local solutions are additional alternatives for the decision makers if global solutions are impracticable. This paper proposes a particle swarm optimizer based on reference point, termed RPPSO, which combines a reference point mechanism and a local solution preserving technique. The reference point strategy is utilized to establish multiple evenly distributed neighborhoods and guide particles to evolve independently in their respective neighborhoods, so as to detect more Pareto solutions in the decision space. The local solution preserving technique is employed to estimate the dominant radius of each front, and with this radius to classify the individuals as either non-local or local solutions with the aim of retaining the local solutions. In addition, a set of benchmark test functions with local Pareto solutions are designed. The proposed algorithm is comprehensively evaluated on forty-four benchmark functions and is compared with fourteen state-of-the-art algorithms. The experimental results show that the proposed RPPSO achieves competitive performance than its competitors in terms of the reciprocal of Pareto sets proximity (rPSP). The RPPSO is also applied to solve on one real-world problem (i.e., map-based problem) to further verify the effectiveness and efficiency.