Critical considerations on angle modulated particle swarm optimisers

Abstract

This article investigates various aspects of angle modulated particle swarm optimisers (AMPSO). Previous attempts at improving the algorithm have only been able to produce better results in a handful of test cases. With no clear understanding of when and why the algorithm fails, improving the algorithm’s performance has proved to be a difficult and sometimes blind undertaking. Therefore, the aim of this study is to identify the circumstances under which the algorithm might fail, and to understand and provide evidence for such cases. It is shown that the general assumption that good solutions are grouped together in the search space does not hold for the standard AMPSO algorithm or any of its existing variants. The problem is explained by specific characteristics of the generating function used in AMPSO. Furthermore, it is shown that the generating function also prevents particle velocities from decreasing, hindering the algorithm’s ability to exploit the binary solution space. Methods are proposed to both confirm and potentially solve the problems found in this study. In particular, this study addresses the problem of finding suitable generating functions for the first time. It is shown that the potential of a generating function to solve arbitrary binary optimisation problems can be quantified. It is further shown that a novel generating function with a single coefficient is able to generate solutions to binary optimisation problems with fewer than four dimensions. The use of ensemble generating functions is proposed as a method to solve binary optimisation problems with more than 16 dimensions.