An optimal representation of Random Maximum kSatisfiability on a Hopfield Neural Network for High order logic(k 3)

Abstract

This paper proposed a new logical rule by incorporating Random maximum kSatsifiability (RANMAXkSAT) in the Hopfield neural network (HNN) as a single network model (HNN-RANMAXkSAT). The purpose is to combine the optimization capacity of the Hopfield neural network (HNN) for optimal representation to random maximum kSatsifiability (MAXRANkSAT). The energy function of a Hopfield neural network has been considered as a programming language for dynamics minimization mechanism. Several optimization and search problems associated with machine learning (ML), decision Science (DS) and artificial intelligence (AI) have been expressed on the Hopfield neural network(HNN) optimally by modelling the problem into variables to minimize the objective function that corresponds to Lyapunov energy function. The computer simulation has been developed based on RANMAXkSAT to explore the feasibility of a Hopfield neural network as a neuro-symbolic integration model in carrying out RANMAXkSAT logic programming optimally. The proposed model has been compared with the existing models published in the literature in term of Global minimum ratio (zM), Fitness energy landscapes (FEL), Root Means square error (RMSE), Mean absolute errors and computation time (CPU). Hence, based on the experimental simulation results, it revealed that the RANMAXkSAT can optimally and effectively represented in the Hopfield neural network (HNN) with 85.1 % classification accuracy.