Piecewise-linear particle swarm optimizer, basic dynamics, reference frame invariance, and search performance

Abstract

Swarm intelligence (SI) algorithms have been studied in solving real-world optimization problems called black-box optimization problems. Typical features of SI algorithms are: (1) being a population-based metaheuristics; (2) using fitness values of a given objective function; and (3) having very simple search rules which search agents follow. As such, SI algorithms have been applied to various black-box optimization problems. Particle swarm optimization is one of powerful SI algorithms, in which a swarm consists of plural particles as solution candidates. Particles directly fly a search space and share their own information each other, and thus PSO can find good quality of solutions. However, a PSO swarm is easily stuck in solving optimization problems whose search space is high-dimensional and complicated. In order to solve such problems, large numbers of particles and reference frame invariance are needed for PSO algorithms. Herein, we suggest a piecewise-linear particle swarm optimizer (PPSO) which is a deterministic PSO. PPSO has two simple search modes switched to an-other mode dynamically, whose search dynamics are complex. As such, PPSO algorithm can be implemented on hardware with low hardware costs because PPSO algorithm must not require many random number generators. In addition, PPSO algorithm can find a good quality of solution in solving complex optimization problems. We studied search performances of PPSO compared to PSO algorithms and provide theoretical analysis of reference frame invariance for PPSO. In order to verify search performances and theoretical analysis, we performed numerical simulations.