Determination of Near-global Optimal Initial Weights of Artificial Neural Network Using Harmony Search Algorithm: Application to Breakwater Armor Stones

Abstract

Artificial neural networks (ANNs) have become a popular tool as the efficient model for prediction and forecast in various areas. Despite a great number of application in numerous researches, ANNs are hardly recognized as a generalized tool because of its characteristics. The back propagation (BP) algorithm helps to find the optimal values of the weights and biases of the neural networks that correspond to the minimum value of a performance function usually defined as the root-mean squared error between output variable and target variable. However, the BP is based on the gradient descent method which can give the local minimum value of a specified function and which is sensitive to the initial values of the weights and biases. To search for the global minimum of the performance function, the Monte-Carlo simulation generating a number of ANNs having different initial weights and biases has been suggested to search the global minimum of the performance function. However, it is not efficient and it takes a long time. In this study, an ANN model is developed to predict the stability number of breakwater armor stones based on the experimental data reported by Van der Meer in 1988. To resolve the fundamental problems in neural networks due to local minimization, the harmony search (HS) algorithm is used. Firstly, the HS algorithm would find the weights which have the near-global minimum of the performance function. The optimized weights found by HS are then used as the initial weights for the ANNs and further modified by the BP algorithm. The BP training based on the gradient descent method would allow fine adjustment of the weights. To assess the reliability of the ANN model with BP training and the ANN-HS model, both models were run 50 times and the statistical analysis was conducted for the model results. Each of harmony memory considering rate (HMCR) and pitch adjustment rate (PAR) of HS has five different values varying from 0.1 to 0.9 at an interval of 0.2. The correlation coefficient and index of agreement between model output values and target values in the validation data were used to evaluate the performance of the models. It was shown that the ANN-HS models with HMCR=0.9 and PAR=0.1 and HMCR=0.7 and PAR=0.5 give more accurate and consistent prediction ability than the general ANN model trained by BP algorithm.