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Markov chain models of bare-bones particle swarm optimizers

Published: 07 July 2007 Publication History

Abstract

We apply a novel theoretical approach to better understand the behaviour of different types of bare-bones PSOs. It avoids many common but unrealistic assumptions often used in analyses of PSOs. Using finite element grid techniques, it builds a discrete Markov chain model of the BB-PSO which can approximate it on arbitrary continuous problems to any precision. Iterating the chain's transition matrix gives precise information about the behaviour of the BB-PSO at each generation, including the probability of it finding the global optimum or being deceived. The predictions of the model are remarkably accurate and explain the features of Cauchy, Gaussian and other sampling distributions.

References

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van den Bergh, F. (2002) An Analysis of Particle Swarm Optimizers. PhD thesis, Department of Computer Science, University of Pretoria, South Africa.
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Clerc, M. (2006) Stagnation analysis in particle swarm optimisation or what happens when nothing happens. Technical Report CSM-460, Department of Computer Science, University of Essex, August 2006.
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W. M. Spears (1998) The Role of Mutation and Recombination in Evolutionary Algorithms. PhD thesis, George Mason University.

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cover image ACM Conferences
GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation
July 2007
2313 pages
ISBN:9781595936974
DOI:10.1145/1276958
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 07 July 2007

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Author Tags

  1. bare-bones PSO
  2. particle swarm optimisation
  3. theory

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GECCO '07 Paper Acceptance Rate 266 of 577 submissions, 46%;
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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  • (2024)A Robust and Efficient Ensemble of Diversified Evolutionary Computing Algorithms for Accurate Robot CalibrationIEEE Transactions on Instrumentation and Measurement10.1109/TIM.2024.336378373(1-14)Online publication date: 2024
  • (2024)Particle Swarm OptimizationHandbook of Heuristics10.1007/978-3-319-07153-4_22-2(1-51)Online publication date: 2-Aug-2024
  • (2023)Hyperparameter Learning for Deep Learning-Based Recommender SystemsIEEE Transactions on Services Computing10.1109/TSC.2023.323462316:4(2699-2712)Online publication date: 1-Jul-2023
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  • (2018)Reprint ofJournal of Computational and Applied Mathematics10.1016/j.cam.2018.04.036340:C(709-717)Online publication date: 1-Oct-2018
  • (2018)On convergence analysis of particle swarm optimization algorithmJournal of Computational and Applied Mathematics10.1016/j.cam.2017.10.026333(65-73)Online publication date: May-2018
  • (2017)Learning Multimodal Parameters: A Bare-Bones Niching Differential Evolution ApproachIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2017.2708712(1-16)Online publication date: 2017
  • (2016)Convergence analysis of brain storm optimization algorithm2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7744264(3747-3752)Online publication date: Jul-2016
  • (2015)Random drift particle swarm optimization algorithmMachine Language10.1007/s10994-015-5522-z101:1-3(345-376)Online publication date: 1-Oct-2015
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