The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
L'optimiseur d'essaim de particules (PSO) est une technique d'optimisation globale stochastique basée sur une métaphore d'interaction sociale. En raison de la complexité, de la dynamique et du caractère aléatoire impliqués dans la PSO, il est difficile d’analyser théoriquement le mécanisme dont dépend la PSO. Les résultats statistiques ont montré que la distribution de probabilité de PSO est un triangle tronqué, avec une probabilité uniforme au milieu qui diminue sur les côtés. Le « triangle tronqué » est aussi appelé « pyramide maya » par Kennedy. Cependant, on sait très peu de choses sur la distribution d’échantillonnage du PSO en soi. Dans cet article, nous analysons théoriquement la « pyramide Maya » sans aucune hypothèse et en déduisons sa formule de calcul, qui est en fait une distribution uniforme hybride qui ressemble à un trapèze et est conforme aux résultats statistiques. Sur la base de la fonction de densité dérivée de la distribution uniforme hybride, la stratégie de recherche de PSO est définie et quantifiée pour caractériser le mécanisme de la stratégie de recherche dans PSO. Afin de montrer l'importance de ces définitions basées sur la distribution uniforme hybride dérivée, la comparaison entre les stratégies de recherche définies du PSO linéaire classique basé sur un poids décroissant et du PSO canonique resserré suggéré par Clerc est illustrée et élaborée.
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Junqi ZHANG, Ying TAN, Lina NI, Chen XIE, Zheng TANG, "Hybrid Uniform Distribution of Particle Swarm Optimizer" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 10, pp. 1782-1791, October 2010, doi: 10.1587/transfun.E93.A.1782.
Abstract: Particle swarm optimizer (PSO) is a stochastic global optimization technique based on a social interaction metaphor. Because of the complexity, dynamics and randomness involved in PSO, it is hard to theoretically analyze the mechanism on which PSO depends. Statistical results have shown that the probability distribution of PSO is a truncated triangle, with uniform probability across the middle that decreases on the sides. The "truncated triangle" is also called the "Maya pyramid" by Kennedy. However, very little is known regarding the sampling distribution of PSO in itself. In this paper, we theoretically analyze the "Maya pyramid" without any assumption and derive its computational formula, which is actually a hybrid uniform distribution that looks like a trapezoid and conforms with the statistical results. Based on the derived density function of the hybrid uniform distribution, the search strategy of PSO is defined and quantified to characterize the mechanism of the search strategy in PSO. In order to show the significance of these definitions based on the derived hybrid uniform distribution, the comparison between the defined search strategies of the classical linear decreasing weight based PSO and the canonical constricted PSO suggested by Clerc is illustrated and elaborated.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1782/_p
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@ARTICLE{e93-a_10_1782,
author={Junqi ZHANG, Ying TAN, Lina NI, Chen XIE, Zheng TANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Hybrid Uniform Distribution of Particle Swarm Optimizer},
year={2010},
volume={E93-A},
number={10},
pages={1782-1791},
abstract={Particle swarm optimizer (PSO) is a stochastic global optimization technique based on a social interaction metaphor. Because of the complexity, dynamics and randomness involved in PSO, it is hard to theoretically analyze the mechanism on which PSO depends. Statistical results have shown that the probability distribution of PSO is a truncated triangle, with uniform probability across the middle that decreases on the sides. The "truncated triangle" is also called the "Maya pyramid" by Kennedy. However, very little is known regarding the sampling distribution of PSO in itself. In this paper, we theoretically analyze the "Maya pyramid" without any assumption and derive its computational formula, which is actually a hybrid uniform distribution that looks like a trapezoid and conforms with the statistical results. Based on the derived density function of the hybrid uniform distribution, the search strategy of PSO is defined and quantified to characterize the mechanism of the search strategy in PSO. In order to show the significance of these definitions based on the derived hybrid uniform distribution, the comparison between the defined search strategies of the classical linear decreasing weight based PSO and the canonical constricted PSO suggested by Clerc is illustrated and elaborated.},
keywords={},
doi={10.1587/transfun.E93.A.1782},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Hybrid Uniform Distribution of Particle Swarm Optimizer
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1782
EP - 1791
AU - Junqi ZHANG
AU - Ying TAN
AU - Lina NI
AU - Chen XIE
AU - Zheng TANG
PY - 2010
DO - 10.1587/transfun.E93.A.1782
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2010
AB - Particle swarm optimizer (PSO) is a stochastic global optimization technique based on a social interaction metaphor. Because of the complexity, dynamics and randomness involved in PSO, it is hard to theoretically analyze the mechanism on which PSO depends. Statistical results have shown that the probability distribution of PSO is a truncated triangle, with uniform probability across the middle that decreases on the sides. The "truncated triangle" is also called the "Maya pyramid" by Kennedy. However, very little is known regarding the sampling distribution of PSO in itself. In this paper, we theoretically analyze the "Maya pyramid" without any assumption and derive its computational formula, which is actually a hybrid uniform distribution that looks like a trapezoid and conforms with the statistical results. Based on the derived density function of the hybrid uniform distribution, the search strategy of PSO is defined and quantified to characterize the mechanism of the search strategy in PSO. In order to show the significance of these definitions based on the derived hybrid uniform distribution, the comparison between the defined search strategies of the classical linear decreasing weight based PSO and the canonical constricted PSO suggested by Clerc is illustrated and elaborated.
ER -