A relationship between network topology and search performance of PSO

Abstract

Particle swarm optimization (abbr. PSO) is one of the most effective optimization algorithms. The PSO contains many control parameters, therefore, the performance of the searching ability of the PSO is significantly alternated. In order to analyze the dynamics of such PSO system rigorously, we have analyzed a deterministic PSO (abbr. D-PSO) systems which does not contain any stochastic factors, and its coordinate of the phase space is normalized. The found global best information influences the dynamics. This situation can be regarded as the full-connection state. On the other hand, there is the case where the best information in a limited population. Such information is called as. How to get the information from any population is equivalent to a network structure. Such network structure influences the performance of searching ability. In order to clarify a relationship between network structures of the PSO and its performance, we pay attention to the degree and the average distance used in graph theory. We consider the two cases where the D-PSO has an extended cycle structure and a Small World network structure. Our numerical simulation results indicates the searching performance of the D-PSO is depended on the average distance of the node. Especially, the long average distance exerts the search performance on the D-PSO. We confirm that the search performance properties of the D-PSO and the conventional stochastic PSO are completely different to the average distance. The search performance of the D-PSO is improved according to the average distance. On the other hand, the search performance of the conventional stochastic PSO is deteriorated according to the average distance. We consider that the slow transmission of the beneficial information leads to the diversification of the particles of the D-PSO. Also, we clarify the small perturbation of the random range of the stochastic PSO is important.

A Novel Method to Find Optimal Solution Based on Modified Butterfly Particle Swarm Optimization

“…The obtained results by BF-PSO are compared to the results obtained by other method [14,[17][18][19][20]33]. Result shows that for benchmark functions the convergence of fitness with S-PSO take more iterations while in BF-PSO function converged fitness value in less iterations; hence the time taken in BF-PSO for optimal value is very less.…”

“…This type of the intelligent network structure influences the performance of searching ability [19].…”

“…In the butterfly network node (flower) having more amounts of nectar will attract more and more butterflies by natural sensitivity [2,27] hence; it will increase the degree of the node (flower) because of that node has higher probability of nectar. The butterflies exchange the information not only by dancing, but also they have natural intelligence for sensing nectar through color, insect, chemical, sound and physical action [28][29][30][31][32], so it develops better communication network compared to others [18][19][20][21]. The formation of the "collective intelligence" in the butterfly network by these different types of communication systems between individual butterflies [24].…”

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“…according to ingeniously and due to antenna on their mouth by tterfly more compare to others [2,19] there is very good relation of butterfly and surrounding atmosphere to provide best solution [19]. After butterfly relinquishes the food, butterfly propagate in the direction of new nectar source or gets information fro others being nectar there so it does not recruits any nest mates like in BCO [2,19].…”

A Nonlinear Blind Source Separation System Using Particle Swarm Optimization Algorithm

“…The information translation structure of particles can be regarded as a network structure. Several researchers have studied the relatioship between the search performance and the network structure [17] [18]. A ring structure is effective for searching for the optimum value of a multimodal function.…”