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.
