Artificial Immune System in Doing 2-Satisfiability Based Reverse Analysis Method via a Radial Basis Function Neural Network

Shehab Abdulhabib Alzaeemi,Saratha Sathasivam

doi:10.3390/pr8101295

Abstract

A radial basis function neural network-based 2-satisfiability reverse analysis (RBFNN-2SATRA) primarily depends on adequately obtaining the linear optimal output weights, alongside the lowest iteration error. This study aims to investigate the effectiveness, as well as the capability of the artificial immune system (AIS) algorithm in RBFNN-2SATRA. Moreover, it aims to improve the output linearity to obtain the optimal output weights. In this paper, the artificial immune system (AIS) algorithm will be introduced and implemented to enhance the effectiveness of the connection weights throughout the RBFNN-2SATRA training. To prove that the introduced method functions efficiently, five well-established datasets were solved. Moreover, the use of AIS for the RBFNN-2SATRA training is compared with the genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and artificial bee colony (ABC) algorithms. In terms of measurements and accuracy, the simulation results showed that the proposed method outperformed in the terms of Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Schwarz Bayesian Criterion (SBC), and Central Process Unit time (CPU time). The introduced method outperformed the existing four algorithms in the aspect of robustness, accuracy, and sensitivity throughout the simulation process. Therefore, it has been proven that the proposed AIS algorithm effectively conformed to the RBFNN-2SATRA in relation to (or in terms of) the average value of training of RMSE rose up to 97.5%, SBC rose up to 99.9%, and CPU time by 99.8%. Moreover, the average value of testing in MAE was rose up to 78.5%, MAPE was rose up to 71.4%, and was capable of classifying a higher percentage (81.6%) of the test samples compared with the results for the GA, DE, PSO, and ABC algorithms.

Highlights

Radial basis function neural network (RBFNN) has been widely used in many fields due to its simpler network structure, faster learning speeds, and better approximation capabilities [1,2]
RBFNN is simpler than multilayer perceptron neural network (MLP) network, which may contain more than three layers of the structure; the process of training in RBFNN is generally faster than MLP [4,5]
Percentage Error (MAPE), Root Mean Square Error (RMSE), and Central Process Unit time (CPU time) showed the structure complexity of RBFNN-2-satisfiability based reverse analysis method (2SATRA) network based on the rising neuron numbers as shown in the following equation: RMSE =

Summary

Introduction

Radial basis function neural network (RBFNN) has been widely used in many fields due to its simpler network structure, faster learning speeds, and better approximation capabilities [1,2]. RBFNN is a feed-forward neural network, which was first utilized by Moody and Darken [3]; they confirmed that the RBFNN has faster learning speed than the multilayer perceptron neural network (MLP). RBFNN is simpler than MLP network, which may contain more than three layers of the structure; the process of training in RBFNN is generally faster than MLP [4,5]. The difficulty of applying the traditional RBFNN lies in training the network, which should include selecting the proper input variables, the number of hidden neurons, and estimating the parameters (centers, widths) of the RBFNN [4]. We used different algorithms to train RBFNN-2SATRA

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Conclusion