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Theory of particle swarm optimization: A survey of the power of the swarm’s potential

Bernd Bassimir

Bernd Bassimir is a doctoral student at the University of Erlangen-Nuremberg, where he already received his Master of Science in Computer Science. His research interests are scheduling problems, with an emphasis on robust optimization under uncertainty and a deeper understanding of the exploration and exploitation properties of Particle Swarm Optimization (PSO).

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, Alexander Raß

Alexander Raß is a doctoral student at the University of Erlangen-Nuremberg, where he already received his Master of Science in Mathematics. His research interests are runtime analysis of algorithms working on discrete domains and convergence analysis of algorithms working on continuous domains. In both cases the focus is on Particle Swarm Optimization (PSO). Additionally he established an open-source project for PSO with very high and adaptive precision.

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and Manuel Schmitt

Manuel Schmitt received his diploma degree in Mathematics from the University of Erlangen-Nuremberg, Germany, in 2011 and his doctorate degree from the same university in 2015. His current affiliation is the Julianum high school in Helmstedt, Germany. His research interests are the satisfiability problem and the analysis of meta-heuristics for black-box optimization problems, particularly the analysis of Particle Swarm Optimization (PSO).

Abstract

This paper presents a survey on different showcases for potential measures on particle swarm optimization (PSO). First, a potential is analyzed to prove convergence to non-optimal points. Second, one can apply a minor modification to PSO to prevent convergence to non-optimal points by using an easy potential measure. Finally, analyzing this potential measure yields a reliable stopping criterion for the modified PSO.

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About the authors

Bernd Bassimir

Bernd Bassimir is a doctoral student at the University of Erlangen-Nuremberg, where he already received his Master of Science in Computer Science. His research interests are scheduling problems, with an emphasis on robust optimization under uncertainty and a deeper understanding of the exploration and exploitation properties of Particle Swarm Optimization (PSO).

Alexander Raß

Alexander Raß is a doctoral student at the University of Erlangen-Nuremberg, where he already received his Master of Science in Mathematics. His research interests are runtime analysis of algorithms working on discrete domains and convergence analysis of algorithms working on continuous domains. In both cases the focus is on Particle Swarm Optimization (PSO). Additionally he established an open-source project for PSO with very high and adaptive precision.

Manuel Schmitt

Manuel Schmitt received his diploma degree in Mathematics from the University of Erlangen-Nuremberg, Germany, in 2011 and his doctorate degree from the same university in 2015. His current affiliation is the Julianum high school in Helmstedt, Germany. His research interests are the satisfiability problem and the analysis of meta-heuristics for black-box optimization problems, particularly the analysis of Particle Swarm Optimization (PSO).

References

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Received: 2019-01-18
Revised: 2019-09-18
Accepted: 2019-10-10
Published Online: 2019-10-19
Published in Print: 2019-08-27

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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