Evaluating center-seeking and initialization bias: The case of particle swarm and gravitational search algorithms

Abstract

Complex optimization problems that cannot be solved using exhaustive search require efficient search metaheuristics to find optimal solutions. In practice, metaheuristics suffer from various types of search bias, the understanding of which is of crucial importance, as it is directly pertinent to the problem of making the best possible selection of solvers. In this paper, two metrics are introduced: one for measuring center-seeking bias (CSB) and one for initialization region bias (IRB). The former is based on “ξ-center offset”, an alternative to “center offset”, which is a common but inadequate approach to analyzing the center-seeking behavior of algorithms, as will be shown. The latter is proposed on the grounds of “region scaling”. The introduced metrics are used to evaluate the bias of three algorithms while running on a test bed of optimization problems having their optimal solution at, or near, the center of the search space. The most prominent finding of this paper is considerable CSB and IRB in the gravitational search algorithm (GSA). In addition, a partial solution to the center-seeking and initialization region bias of GSA is proposed by introducing a “mass-dispersed” version of GSA, mdGSA. mdGSA promotes the global search capability of GSA. Its performance is verified using the same mathematical optimization problem, next to a gene regulatory network parameter identification problem. The results of these experiments demonstrate the capabilities of mdGSA in solving real-world optimization problems.