Election Algorithm for Random k Satisfiability in the Hopfield Neural Network

Abstract

Election Algorithm (EA) is a novel variant of the socio-political metaheuristic algorithm, inspired by the presidential election model conducted globally. In this research, we will investigate the effect of Bipolar EA in enhancing the learning processes of a Hopfield Neural Network (HNN) to generate global solutions for Random k Satisfiability (RANkSAT) logical representation. Specifically, this paper utilizes a bipolar EA incorporated with the HNN in optimizing RANkSAT representation. The main goal of the learning processes in our study is to ensure the cost function of RANkSAT converges to zero, indicating the logic function is satisfied. The effective learning phase will affect the final states of RANkSAT and determine whether the final energy is a global minimum or local minimum. The comparison will be made by adopting the same network and logical rule with the conventional learning algorithm, namely, exhaustive search (ES) and genetic algorithm (GA), respectively. Performance evaluation analysis is conducted on our proposed hybrid model and the existing models based on the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Sum of Squared Error (SSE), and Mean Absolute Error (MAPE). The result demonstrates the capability of EA in terms of accuracy and effectiveness as the learning algorithm in HNN for RANkSAT with a different number of neurons compared to ES and GA.