Particle swarm optimization: Difference between revisions

Revision as of 04:29, 5 August 2023

Revision as of 10:22, 23 August 2023

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* Convergence to a local optimum where all personal bests '''p''' or, alternatively, the swarm's best known position '''g''', approaches a local optimum of the problem, regardless of how the swarm behaves.

Convergence of the sequence of solutions has been investigated for PSO.<ref name=bergh01thesis/><ref name=clerc02explosion/><ref name=trelea03particle/> These analyses have resulted in guidelines for selecting PSO parameters that are believed to cause convergence to a point and prevent divergence of the swarm's particles (particles do not move unboundedly and will converge to somewhere). However, the analyses were criticized by Pedersen<ref name=pedersen08simplifying/> for being oversimplified as they assume the swarm has only one particle, that it does not use stochastic variables and that the points of attraction, that is, the particle's best known position '''p''' and the swarm's best known position '''g''', remain constant throughout the optimization process. However, it was shown<ref>{{cite journalbook|last1=Cleghorn|first1=Christopher W|title=Swarm Intelligence |chapter=Particle Swarm Convergence: Standardized Analysis and Topological Influence|journal=Swarm Intelligence Conference|volume=8667|pages=134–145|date=2014|doi=10.1007/978-3-319-09952-1_12|series=Lecture Notes in Computer Science|isbn=978-3-319-09951-4}}</ref> that these simplifications do not affect the boundaries found by these studies for parameter where the swarm is convergent. Considerable effort has been made in recent years to weaken the modelling assumption utilized during the stability analysis of PSO,<ref name=Liu2015/> with the most recent generalized result applying to numerous PSO variants and utilized what was shown to be the minimal necessary modeling assumptions.<ref name=Cleghorn2018/>

Convergence to a local optimum has been analyzed for PSO in<ref>{{cite journal|last1=Van den Bergh|first1=F|title=A convergence proof for the particle swarm optimiser|journal=Fundamenta Informaticae|url=https://repository.up.ac.za/bitstream/handle/2263/17262/VanDenBergh_Convergence(2010).pdf?sequence=1}}</ref> and.<ref name=Bonyadi2014/> It has been proven that PSO needs some modification to guarantee finding a local optimum.

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<ref name="tu04corrections">{{cite journal | first1=Z. | last1=Tu | title=Corrections to "A Robust Stochastic Genetic Algorithm (StGA) for Global Numerical Optimization'' | last2=Lu | first2=Y. | journal=IEEE Transactions on Evolutionary Computation | year=2008 | volume=12 | issue=6 | pages=781 | doi=10.1109/TEVC.2008.926734| s2cid=2864886 }}</ref>

<ref name="meissner06optimized">{{cite journal | first1=M. | last1=Meissner | title=Optimized Particle Swarm Optimization (OPSO) and its application to artificial neural network training | last2=Schmuker | first2=M. | last3=Schneider | first3=G. | journal=BMC Bioinformatics | pmc=1464136 | year=2006 | volume=7 | issue=1 | pages=125 | doi=10.1186/1471-2105-7-125 | pmid=16529661 | doi-access=free }}</ref>

<ref name="yang08nature">{{cite book | first1=X.S. | last1=Yang | title=Nature-Inspired Metaheuristic Algorithms | publisher=Luniver Press | year=2008 | isbn=978-1-905986-10-1}}</ref>

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<ref name="kennedy2002population">{{cite book | first1=J. | last1=Kennedy | last2=Mendes | first2=R. | date=2002 | title=Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600) | chapter=Population structure and particle swarm performance | volume=2 | pages=1671–1676 vol.2 | year=2002 | doi=10.1109/CEC.2002.1004493| isbn=978-0-7803-7282-5 | citeseerx=10.1.1.114.7988 | s2cid=14364974 }}</ref>

<ref name="oliveira2016communication">{{cite book | first1=M. | last1=Oliveira | title=Communication Diversity in Particle Swarm Optimizers | last2=Pinheiro | first2=D. | last3=Andrade | first3=B. | last4=Bastos-Filho | first4=C. | last5=Menezes | first5=R. | journaltitle=InternationalSwarm ConferenceIntelligence on| chapter=Communication Diversity in Particle Swarm IntelligenceOptimizers | volume=9882 | year=2016 | pages=77–88 | doi=10.1007/978-3-319-44427-7_7| series=Lecture Notes in Computer Science | isbn=978-3-319-44426-0 | s2cid=37588745 | url=https://semanticscholar.org/paper/4a4bf82f6152d81a83a695fd7e063248f8d42e83 }}</ref>

<ref name="cazzaniga2015">{{cite conference | first1=P. | last1=Cazzaniga | title=The impact of particles initialization in PSO: parameter estimation as a case in point, (Canada) | last2=Nobile | first2=M.S. | last3=Besozzi | first3=D. | book-title=Proceedings of IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology | year=2015| doi=10.1109/CIBCB.2015.7300288 }}</ref>