Deception, blindness and disorientation in particle swarm optimization applied to noisy problems

Abstract

Particle swarm optimization (PSO) is a population-based algorithm designed to find good solutions to optimization problems. However, if the problems are subject to noise, the quality of its results significantly deteriorates. Previous works have addressed such a deterioration by developing noise mitigation mechanisms to target specific issues such as handling the inaccurate memories of the particles and aiding the particles to correctly select their neighborhood best solutions. However, in spite of the improvements achieved, it still remains uncertain the extent to which these issues affect the particles, and the underlying reasons for the deterioration of the quality of the results. In this article, we formally define deception, blindness and disorientation as the conditions responsible for such a deterioration, and we develop a set of population statistics to measure the extent to which these conditions affect the particles throughout the search process. The population statistics are computed for the regular PSO algorithm and for PSO with equal resampling (PSO-ER) on 20 large-scale benchmark functions subject to different levels of multiplicative Gaussian noise. The key findings that we reveal with the population statistics on optimization problems subject to noise are the following: (a) the quality of the results significantly deteriorates as particles suffer from large proportions of deception and blindness; (b) the presence of deception, blindness and disorientation, and their effects on the quality of results, makes the performance Electronic supplementary material The online version of this article (123 248 Swarm Intell (2014) 8:247-273of the swarms sensitive to optimization problems subject to noise; (c) the incorporation of resampling methods into PSO significantly improves the quality of the results; and (d) it is better to first address the conditions of blindness and disorientation before addressing deception.

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

“…The PSO and DE algorithms are chosen in this study due to their large popularity and versatile applications in various fields of science. The interested reader may find details on both families of methods in numerous reviews or books (Price et al 2005;Clerc 2006;Poli et al 2007;Banks et al 2008;Das et al 2008Das et al , 2016Neri and Tirronen 2010;Das and Suganthan 2011;Xin et al 2012;Rada-Vilela et al 2014;Zhang et al 2015;Piotrowski 2016;Bonyadi and Michalewicz 2016).…”

“…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.…”

Population statistics for particle swarm optimization: Hybrid methods in noisy optimization problems

“…As such, the objective function values of the solutions are underestimated or overestimated, rarely reflecting their true values, and causing a significant deterioration to the performance of metaheuristics, in particular that of PSO [16]. In controlled environments, the effect of noise is usually modeled by sampling noise from a Gaussian distribution [34], whose standard deviation and effect on the objective function values determine the severity of noise.…”

“…In this type of problems, the objective function values that determine the quality of the solutions are corrupted by the effect of sampling noise, hence resulting in differently estimated objective function values every time the solutions are evaluated. As a consequence, particles eventually fail to distinguish good from bad solutions, leading to three conditions known as deception, blindness and disorientation [16]. Particles suffer from deception when they fail to select their true neighborhood best solutions, from blindness when they ignore truly better solutions, and from disorientation when they prefer truly worse solutions.…”

“…Recently, resampling-based and single-evaluation PSO algorithms have been studied by means of a set of population statistics that measure different characteristics of the swarms throughout the search process [16,17,22,28]. The population statistics have revealed that swarms often suffer from deception, blindness and disorientation, for which different algorithms have been designed to reduce the presence of these conditions and hence improve the quality of their resulting solutions.…”