Leboucher, CedricShin, HyosangSiarry, PatrickLe Menec, StephanieChelouah, RachidTsourdos, Antonios2016-08-152016-08-152016-01-08Cédric Leboucher, Hyo-Sang Shin, Patrick Siarry, Stéphane Le Ménec, Rachid Chelouah, Antonios Tsourdos, Convergence proof of an enhanced Particle Swarm Optimisation method integrated with Evolutionary Game Theory, Information Sciences, Volumes 346–347, 10 June 2016, Pages 389-4110020-0255http://dx.doi.org/10.1016/j.ins.2016.01.011.https://dspace.lib.cranfield.ac.uk/handle/1826/10306This paper proposes an enhanced Particle Swarm Optimisation (PSO) algorithm and examines its performance. In the proposed PSO approach, PSO is combined with Evolutionary Game Theory to improve convergence. One of the main challenges of such stochastic optimisation algorithms is the difficulty in the theoretical analysis of the convergence and performance. Therefore, this paper analytically investigates the convergence and performance of the proposed PSO algorithm. The analysis results show that convergence speed of the proposed PSO is superior to that of the Standard PSO approach. This paper also develops another algorithm combining the proposed PSO with the Standard PSO algorithm to mitigate the potential premature convergence issue in the proposed PSO algorithm. The combined approach consists of two types of particles, one follows Standard PSO and the other follows the proposed PSO. This enables exploitation of both diversification of the particles’ exploration and adaptation of the search direction.enAttribution-Non-Commercial-No Derivatives 3.0 Unported (CC BY-NC-ND 3.0). You are free to: Share — copy and redistribute the material in any medium or format. The licensor cannot revoke these freedoms as long as you follow the license terms. Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. Information: Non-Commercial — You may not use the material for commercial purposes. No Derivatives — If you remix, transform, or build upon the material, you may not distribute the modified material. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.Particle Swarm OptimisationEvolutionary Game TheoryLocal optimalityConvergence proofConvergence speedArticle2919169