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 have 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.

Searching for structural bias in particle swarm optimization and differential evolution algorithms

“…Although in this study we pay attention mostly to the problem of structural bias in the algorithms (Kononova et al 2015), it is useful to place our discussion in a broader context. First of all, the abundance of metaheuristics that are frequently developed without any theoretical justification leads to at least three undesired effects: (i) it is hard to properly choose the right method for a particular task (Muñoz et al 2015;Yuen and Zhang 2015); (ii) although performance of some widely used metaheuristics is promising, many others show little (if any) novelty and efficiency-instead they rather compete for popularity by using appealing nomenclature (Sörensen 2015); (iii) even though studies of the behaviour of metaheuristics do appear (Clerc and Kennedy 2002;Van den Bergh and Engelbrecht 2004;Auger and Doerr 2011;Liao et al 2013;Bonyadi and Michalewicz 2014;Cleghorn and Engelbrecht 2014;Hu et al 2014;Rada-Vilela et al 2014;Leonard et al 2015;Hu et al 2016), in the majority of papers a desire to propose yet another novel optimizer dominates over the willingness to gain deeper insight into the already available methods. This fact, combined with a lack of commonly accepted procedures to properly develop, study and compare metaheuristics [see for example the discussion in Michalewicz 2012 andSörensen et al 2015], triggered a number of critical research outputs that identified many important issues.…”

A db-Scan Hybrid Algorithm: An Application to the Multidimensional Knapsack Problem

“…To carry out the different experiments, the PSO and CS algorithms were used. They were chosen mainly because they are simple to parameterize, both have successfully solved a large number of optimization problems [2,5,[80][81][82], and there are simplified convergence models for CS [83] and PSO [56].…”

“…In [57], we analyzed how TFs altered the exploration and exploitation process. We also find an analysis of these properties in [56], for the angle modulation technique.…”

“…The main challenge a binarization framework has to tackle is associated with spatial disconnection [56]. When two solutions that are close in continuous space are not close in binary space when applying the binarization process, a spatial disconnection occurs.…”

Putting Continuous Metaheuristics to Work in Binary Search Spaces

“…This exploration of new binarizations is very powerful if it is accompanied by analysis of positions and velocities of particles of the system to understand the conditions in which angle modulation works properly. As a suggestion we propose reading the work done in [124] in PSO.…”