A hybrid simultaneous perturbation artificial bee colony and back-propagation algorithm for training a local linear radial basis neural network on ore grade estimation

Abstract

In this paper, a local linear radial basis function (LLRBF) neural network that uses a skewed Gaussian activation function, called LLRBF-SG, is applied to the problem of ore grade estimation of highly skewed data from the Esfordi phosphate deposit. The network is trained using SPABC-BP, a method that combines a novel simultaneous perturbation artificial bee colony algorithm (SPABC) and back-propagation (BP) method. The SPABC algorithm is an extension of the standard artificial bee colony (ABC) algorithm that includes a tournament selection strategy, simultaneous perturbation stochastic approximation method and new search equations. The predictive accuracy of the network trained with the SPABC-BP algorithm is compared with hybrid versions of evolutionary and swarm intelligence algorithms, such as standard artificial bee colony, covariance matrix adaptation evolution strategy (CMAES) and particle swarm optimization (PSO) with BP. From the experimental results one concludes that networks trained with the SPABC-BP algorithm outperform networks trained with the alternative algorithms in the process of ore grade estimation. The predictive accuracy of the LLRBF-SG-SPABC-BP is compared with LLRBF-SPABC-BP and standard radial basis function (RBF) trained with SPABC-BP algorithm. An analysis of the results shows that the proposed LLRBF-SG network has higher generalization ability and is better suited to the problem of predicting ore grade values for highly skewed data.