Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm

Jiang, Minghu; Luo, Yi; Yang, Shiyuan

doi:10.1016/j.ipl.2006.10.005

Cited by 426 publications

(249 citation statements)

References 6 publications

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“…Since the convergence analysis in [8] implies that the general movement of a converging particle swarm drops exponentially, a logarithmic scale is used and linear decrease is expected.…”

Section: Potential and Stagnation Phasesmentioning

confidence: 99%

Explanation of Stagnation at Points that are not Local Optima in Particle Swarm Optimization by Potential Analysis

Raß

Schmitt

Wanka

2015

Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Particle Swarm Optimization (PSO) is a nature-inspired meta-heuristic for solving continuous optimization problems. In [16,18], the potential of the particles of a swarm has been used to show that slightly modified PSO guarantees convergence to local optima. Here we show that under specific circumstances the unmodified PSO, even with swarm parameters known (from the literature) to be "good", almost surely does not yield convergence to a local optimum is provided. This undesirable phenomenon is called stagnation. For this purpose, the particles' potential in each dimension is analyzed mathematically. Additionally, some reasonable assumptions on the behavior of the particles' potential are made. Depending on the objective function and, interestingly, the number of particles, the potential in some dimensions may decrease much faster than in other dimensions. Therefore, these dimensions lose relevance, i. e., the contribution of their entries to the decisions about attractor updates becomes insignificant and, with positive probability, they never regain relevance. If Brownian Motion is assumed to be an approximation of the time-dependent drop of potential, practical, i. e., large values for this probability are calculated. Finally, on chosen multidimensional polynomials of degree two, experiments are provided showing that the required circumstances occur quite frequently. Furthermore, experiments are provided showing that even when the very simple sphere function is processed the described stagnation phenomenon occurs. Consequently, unmodified PSO does not converge to any local optimum of the chosen functions for tested parameter settings.

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“…Since the convergence analysis in [8] implies that the general movement of a converging particle swarm drops exponentially, a logarithmic scale is used and linear decrease is expected.…”

Section: Potential and Stagnation Phasesmentioning

confidence: 99%

Explanation of Stagnation at Points that are not Local Optima in Particle Swarm Optimization by Potential Analysis

Raß

Schmitt

Wanka

2015

Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation

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show abstract

“…• In [15], a convergence-related parameter adjustment scheme (CRPAS) has been proposed based on the convergence condition [9] of the PSO algorithm. In the reference, 9 time-varying parameter schemes are investigated in the numerical experiments, and two schemes among them outperforms the others including the LDIWM and TVAC.…”

Section: Analysis Of Pso Algorithms With Time-varying Parametersmentioning

confidence: 99%

“…However, these approaches make assumptions that the random variables either are constant or have some deterministic constraints, which leads to the limitations of the results. In contrast, the analysis results in [9,10] have been derived without such an assumption. As a result, the parameter region in [9,10] for the PSO algorithm to converge is very similar to the parameter region in [11] empirically derived from many numerical experiments.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, the analysis results in [9,10] have been derived without such an assumption. As a result, the parameter region in [9,10] for the PSO algorithm to converge is very similar to the parameter region in [11] empirically derived from many numerical experiments. Therefore, we have to deal with the random variables as in [9,10] to evaluate the behavior of the PSO algorithm…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Particle Swarm Optimization Algorithms with Multiswarms and Time-Varying Parameters

Wakasa

Ohno

Tanaka

et al. 2011

Stochastic Systems Theory and its Applications (SSS)

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Recently, many kinds of particle swarm optimization (PSO) algorithms have been proposed to improve the performance of the standard one. However, the systematic analysis of the behavior of such algorithms is not sufficient. This paper extends the previous analysis results for the standard PSO algorithm to two types of PSO algorithms. The one is a PSO algorithm with multiswarms, and its properties of decay rate and l 2 gain are analyzed. The decay rate and l 2 gain are closely related to the convergence speed and swarm diversity, respectively, of the algorithm, which also corresponds to exploitation and exploration abilities. The other one is the type of PSO algorithm with time-varying parameters. The characteristics of the parameter settings are investigated from the viewpoints of the convergence speed and swarm diversity.

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“…The swarm technique has proven to outperform GA due to many reasons. Actually, through a good selection of the swarm parameters, the rate of convergence can be controlled [16,17]. Also, it is simpler than GA and much easier to be adjusted to obtain faster convergence [18,19].…”

Section: Introductionmentioning

confidence: 99%

Inversion of Lossy Dielectric Profiles Using Particle Swarm Optimization

Shaltout¹,

Hashish²,

Hassan³

2009

PIER M

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Abstract-An electromagnetic inversion method is proposed for the reconstruction of lossy dielectric slabs. The inversion is done using particle swarm optimization hybridized with Quasi-Newton algorithm. The inversion process is applied to reconstruct dielectric slabs with discrete or continuous profiles. Accurate reconstruction of lossy dielectric slabs is obtained from inversion of reflection coefficient data of normally incident plane waves in the specified frequency range.The proposed algorithm is also tested using noisy data and showed satisfactory performance.

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Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm

Cited by 426 publications

References 6 publications

Explanation of Stagnation at Points that are not Local Optima in Particle Swarm Optimization by Potential Analysis

Explanation of Stagnation at Points that are not Local Optima in Particle Swarm Optimization by Potential Analysis

Analysis of Particle Swarm Optimization Algorithms with Multiswarms and Time-Varying Parameters

Inversion of Lossy Dielectric Profiles Using Particle Swarm Optimization

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