A new initialization technique in polar coordinates for Particle Swarm Optimization and Polar PSO

Abstract

Particle Swarm Optimization (PSO) is one of the famous algorithms inspired by the natural behavior of a swarm (particles). However, it is used to solve n-dimensional problems in search space. One of its modified versions a Polar Particle Swarm Optimizer, was operated in polar coordinates by using an appropriate mapping function introduced based on polar coordinates. The modified algorithm faced some problems, such as generating a distorted search space, which may have been caused by the method of randomization. This paper introduces an initialization technique that operates entirely in polar coordinates. Moreover, an investigation based on standard PSO was done to test the proposed technique. The second part was to use the new initialization technique to enhance the polar PSO performance. In addition, the proposed techniques show evenly distributed points in the polar search space. Furthermore, experimental results were obtained by using various benchmark test functions on different settings of dimensions. While its shows a little enhancement in some benchmark test functions in both PSO and polar PSO, statistically there are no significant differences by using the analysis of variance (ANOVA).