Convergence Analysis of a New MaxMin-SOMO Algorithm
The convergence analysis of MaxMin-SOMO algorithm is presented. The SOM-based optimization (SOMO) is an optimization algorithm based on the self-organizing map (SOM) in order to find a winner in the network. Generally, through a competitive learning process, the SOMO algorithm searches for the minimum of an objective function. The MaxMin-SOMO algorithm is the generalization of SOMO with two winners for simultaneously finding two winning neurons i.e., first winner stands for minimum and second one for maximum of the objective function. In this paper, the convergence analysis of the MaxMin-SOMO is presented. More specifically, we prove that the distance between neurons decreases at each iteration and finally converge to zero. The work is verified with the experimental results.
KeywordsOptimization self organizing map (SOM) SOM-based optimization (SOMO) algorithm particle swarm optimization (PSO) genetic algorithms (GAs)
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This work was supported by National Natural Science Foundation of China (Nos. 11171367 and 61502068), the Fundamental Research Funds for the Central Universities of China (No. 3132014094), the China Postdoctoral Science Foundation (Nos. 2013M541213 and 2015T80239) and Fundacao da Amaro a Pesquisa do Estado de Sao Paulo (FAPESP) Brazil (No. 2012/23329-5).
The authors wish to thank the associate editor and the anonymous reviewers for their helpful and interesting comments. We are very grateful to professor Wu Wei for extremely helpful discussion and comments to improve the quality of the paper. Thanks to professor Ricardo Zorzetto Nicoliello Vêncio for his help to improve the text of the paper.
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