Convergence analysis of a new self organizing map based optimization (SOMO) algorithm

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.