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Type: Conference paper
Title: SPSO2011 - Analysis of stability, local convergence, and rotation sensitivity
Author: Bonyadi, M.
Michalewicz, Z.
Citation: Proceedings of the 2014 Genetic and Evolutionary Computation Conference, 2014 / Igel, C. (ed./s), pp.9-15
Publisher: Association for Computing Machinery
Issue Date: 2014
ISBN: 9781450326629
Conference Name: 2014 Genetic and Evolutionary Computation Conference (GECCO '14) (12 Jul 2014 - 16 Jul 2014 : Vancouver, Canada)
Statement of
Mohammad Reza Bonyadi, Zbigniew Michalewicz
Abstract: In a particle swarm optimization algorithm (PSO) it is essential to guarantee convergence of particles to a point in the search space (this property is called stability of particles). It is also important that the PSO algorithm converges to a local optimum (this is called the local convergence property). Further, it is usually expected that the performance of the PSO algorithm is not affected by rotating the search space (this property is called the rotation sensitivity). In this paper, these three properties, i.e. stability of particles, local convergence, and rotation sensitivity are investigated for a variant of PSO called Standard PSO2011 (SPSO2011). We experimentally define boundaries for the parameters of this algorithm in such a way that if the parameters are selected in these boundaries, the particles are stable, i.e. particles converge to a point in the search space. Also, we show that, unlike earlier versions of PSO, these boundaries are dependent on the number of dimensions of the problem. Moreover, we show that the algorithm is not locally convergent in general case. Finally, we provide a proof and experimental evidence that the algorithm is rotation invariant.
Keywords: Particle swarm optimization, stability analysis, local convergence, rotation invariance
Rights: Copyright 2014 ACM. 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.
RMID: 0030022054
DOI: 10.1145/2576768.2598263
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