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Particle Swarm Optimization with Single Particle Repulsivity for Multi-modal Optimization

Part of the Lecture Notes in Computer Science book series (LNAI,volume 10841)


This work presents a simple but effective modification of the velocity updating formula in the Particle Swarm Optimization algorithm to improve the performance of the algorithm on multi-modal problems. The well-known issue of premature swarm convergence is addressed by a repulsive mechanism implemented on a single-particle level where each particle in the population is partially repulsed from a different particle. This mechanism manages to prolong the exploration phase and helps to avoid many local optima. The method is tested on well-known and typically used benchmark functions, and the results are further tested for statistical significance.


M. Pluhacek—This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme Project no. LO1303 (MSMT-7778/2014), further by the European Regional Development Fund under the Project CEBIA-Tech no. CZ.1.05/2.1.00/03.0089 and by Internal Grant Agency of Tomas Bata University under the Projects no. IGA/CebiaTech/2018/003. This work is also based upon support by COST (European Cooperation in Science & Technology) under Action CA15140, Improving Applicability of Nature-Inspired Optimisation by Joining Theory and Practice (ImAppNIO), and Action IC1406, High-Performance Modelling and Simulation for Big Data Applications (cHiPSet). The work was further supported by resources of A.I. Lab at the Faculty of Applied Informatics, Tomas Bata University in Zlin (

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Pluhacek, M., Senkerik, R., Viktorin, A., Kadavy, T. (2018). Particle Swarm Optimization with Single Particle Repulsivity for Multi-modal Optimization. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2018. Lecture Notes in Computer Science(), vol 10841. Springer, Cham.

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