Convergence Analysis of a New Self Organizing Map Based Optimization (SOMO) Algorithm

Abstract

The self-organizing map (SOM) approach has been used to perform cognitive and biologically inspired computing in a growing range of cross-disciplinary fields. Recently, the SOM based neural network framework was adapted to solve continuous derivative-free optimization problems through the development of a novel algorithm, termed SOM-based optimization (SOMO). However, formal convergence questions remained unanswered which we now aim to address in this paper. Specifically, convergence proofs are developed for the SOMO algorithm using a specific distance measure. Numerical simulation examples are provided using two benchmark test functions to support our theoretical findings, which illustrate that the distance between neurons decreases at each iteration and finally converges to zero. We also prove that the function value of the winner in the network decreases after each iteration. The convergence performance of SOMO has been benchmarked against the conventional particle swarm optimization algorithm, with preliminary results showing that SOMO can provide a more accurate solution for the case of large population sizes.

Dove Swarm Optimization Algorithm

“…They are expressed in mathematical way as follows [26][27][28][29] (19) The global minimum of Giunta is near 0.9, and all others is zero. For the comparison purpose, we also utilize the GA, the PSO algorithm, and some other 15 existing popular methods such as SOC 1 [30,31], SOC 2 [30,31], DSPSO [32][33][34], FAPSO 1, FAPSO 2, and arPSO [32][33][34], SFS [35], MCS [35,36], GSA [35,37], ABC [35,38], DHS [39], CKH [40], MBO [41], IHS [40], and HS [40] to test these six functions. The results are in Tables 1-6.…”

Bibliometric analysis of patent infringement retrieval model based on self-organizing map neural network algorithm

“…After careful comparison, the patent authorization is determined. As research and development personnel of the enterprise, before the production of new products, it is necessary to conduct patent infringement detection and analysis on patent information in related technical fields (Khan et al, 2015). The patent licensing situation and patent application trends in the related art are well understood.…”