Niching particle swarm optimization with equilibrium factor for multi-modal optimization

Abstract

Multi-modal optimization is an active research topic that has attracted increasing attention from evolutionary computation community. Particle swarm optimization (PSO) with niching technique is one of the most effective approaches for multi-modal optimization. However, in existing PSO with niching methods, the number of particles around different niches varies distinctly from each other, which makes it difficult for the algorithm to find high-quality solutions in all niches. To address this issue, this paper proposes a new niching PSO with equilibrium factor named E-SPSO. Different from the existing niching PSOs, the numbers of particles in different niches have been kept in balance in E-SPSO. The velocity of each particle is influenced by not only the personal best particle and the global best particle, but also an equilibrium factor (EF). By using the equilibrium factor to update the velocities of particles, the particles can be allocated uniformly among the niches. In this way, the computation resources can be assigned to the niches in a more balanced manner, so that the algorithm can gain more population diversity and find high-quality solutions in all niches. Experimental results on eleven benchmark problems show that the proposed mechanism not only increases the number of optima found, but also improves the search efficiency.