Wilcoxon Neural Networks Training Using Evolutionary Optimization Methods

Abstract

In this paper, two kinds of evolutionary computations including a genetic algorithm (GA) and a particle swarm optimization (PSO) are used to train the novel Wilcoxon neural networks (WNNs) for function approximation with outliers. Unlike the traditional artificial neural networks (ANNs), the objective function used in the proposed WNNs is the Wilcoxon norm instead of the total sum of squared errors, i.e., 2-norm. The advantage of using the Wilcoxon norm is to reduce the influence of outliers on overall neural network training. Moreover, to overcome the drawback due to the back-propagation learning algorithm, we utilize the population-based optimization methods containing GA and PSO algorithms to find the suitable weights of WNNs. Finally, some numerical examples, as compared with traditional ANNs, will be provided to verify the robustness against outliers by the proposed methods.