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Soft Computing

, Volume 19, Issue 9, pp 2691–2716 | Cite as

Population statistics for particle swarm optimization: Single-evaluation methods in noisy optimization problems

  • Juan Rada-VilelaEmail author
  • Mark Johnston
  • Mengjie Zhang
Methodologies and Application

Abstract

Particle swarm optimization (PSO) is a metaheuristic whose quality of results deteriorates significantly in optimization problems subject to noise. The underlying reason to such a deterioration is that the effect of noise hinders the ability of particles to distinguish good from bad solutions, leading them to suffer from deception, blindness and disorientation. A deceived particle is not partially attracted to the true best solution in its neighborhood, a blinded particle misses an opportunity to improve upon its personal best solution, and a disoriented particle mistakenly prefers a worse solution. These conditions need to be addressed via noise mitigation mechanisms to prevent (or at least reduce) such a deterioration. Single-evaluation methods are the name by which we refer to PSO algorithms that address the effect of noise without performing additional function evaluations. The first of these algorithms was PSO with evaporation (PSO-E), which was proposed to reduce blindness in the swarms, and reports have suggested that it succeeds at finding better solutions than the regular PSO in different stochastic and dynamic optimization problems. However, PSO-E depends on an evaporation factor whose value is determined empirically, and the swarm is always at risk of exhibiting divergent behaviour. In this article, we propose a method to determine a priori the evaporation factor for PSO-E, and we also propose a new PSO with probabilistic updates (PSO-PU) to prevent the risk of divergence. Additionally, we take a different approach and develop a new PSO with average neighborhoods (PSO-AN) to blur the effect of noise and thereby reduce deception. Experiments on 20 large-scale benchmark functions subject to different levels of noise show that the regular PSO (lacking a noise mitigation mechanism) generally finds better solutions than PSO-E and PSO-PU because their approaches cause too much disorientation. However, PSO-AN finds better solutions than the regular PSO thanks to the improved quality of its neighborhood best solutions that partially attract the swarm towards better regions of the search space.

Keywords

Particle swarm optimization Population statistics  Noisy optimization problems Single-evaluation methods Evaporation mechanism 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Juan Rada-Vilela
    • 1
    • 2
    Email author
  • Mark Johnston
    • 1
    • 3
  • Mengjie Zhang
    • 1
    • 2
  1. 1.Evolutionary Computation Research GroupVictoria University of WellingtonWellingtonNew Zealand
  2. 2.School of Engineering and Computer ScienceVictoria University of WellingtonWellingtonNew Zealand
  3. 3.School of Mathematics, Statistics and Operations ResearchVictoria University of WellingtonWellingtonNew Zealand

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