Weighted Random k Satisfiability for [formula omitted] (r2SAT) in Discrete Hopfield Neural Network

Abstract

Current studies on non-systematic satisfiability in Discrete Hopfield Neural Network are able to avoid production of repetitive final neuron states which improves the quality of global solutions retrieved. This finding has made it possible to obtain diverse final neuron states without additional modifications in Discrete Hopfield Neural Network. However, non-systematic satisfiability exhibited a drawback for neglecting the distribution of positive and negative literals in the logical structure as a neuron representation. Thus, this paper considers a new class of non-systematic satisfiability logic named Weighted Random k Satisfiability for k=1,2 with an inclusive of weighted ratio of negative literals. A logic phase is proposed as an organized layer to assign the distribution of negative literals unbiasedly by using Genetic Algorithm. The performance of Genetic Algorithm in producing the right structure of Weighted Random k Satisfiability will be compared with exhaustive search. Additionally, the training capability of Discrete Hopfield Neural Network to minimize the cost function will be investigated by embedding state of the art metaheuristics. Overall analysis demonstrated the effect of different ratios of negative literals and advanced training algorithm positively impacted the synaptic weight management and production of global minima solutions.