Gaussian Versus Cauchy Membership Functions in Fuzzy PSO

Abstract

In standard particle swarm optimization (PSO), the best particle in each neighborhood exerts its influence over other particles in the neighborhood. Fuzzy PSO is a generalization which differs from standard PSO in the following respect: charisma (influence over others) is defined to be a fuzzy variable, and more than one particle in each neighborhood can have a non-zero degree of charisma, and, consequently, is allowed to influence others to a degree that depends on its charisma. In this paper, we compare between the use of the Gaussian and Cauchy membership functions (MF) as the MF of the charisma fuzzy variable. We evaluate the performance of the two MFs using the weighted max-sat problem.