Fuzzy particle swarm optimization with nearest-better neighborhood for multimodal optimization

In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing performance. Hence, this paper has two main contributions. First, two novel parameter-free neighborhood structures named Topological Nearest-Better (TNB) neighborhood and Distance-based Nearest-Better (DNB) neighborhood are proposed in the topological space and decision space, respectively. Second, two proposed neighborhoods are combined with Fuzzy PSO (FPSO) and two novel niching algorithms, called TNB-FPSO and DNB-FPSO, are proposed for solving multimodal optimization problems. It should be noted that we use a zero-order fuzzy system to balance between exploration and exploitation in the proposed algorithms. To evaluate the performance of proposed algorithms, we performed a detailed empirical evaluation on the several standard multimodal benchmark functions. Our results show that DNB-FPSO statistically outperforms the other compared multimodal optimization algorithms.