Optimising 2SAT Problem Resolution Through Metaheuristic-Driven Hybrid Models of Fuzzy Logic and Hopfield Neural Networks

Abstract

This study addresses the limitations of traditional Boolean-based methods for solving 2SAT problems, which mainly classify variables as true or false and struggle with imprecise information and local minima in Hopfield Neural Networks (HNN). To overcome this challenge, we developed a novel approach that integrates fuzzy logic with HNN, introducing flexibility by permitting the network to handle partial truths during the learning phase. To further enhance this approach, we incorporated Simulated Annealing (SA) and Modified Grey Wolf Optimization (MGWO) to improve the network’s ability to escape local minima and find optimal solutions. We developed three hybrid models: HNN2SATFuzzy, HNN2SATFuzzySA, and HNN2SATFuzzyMGWO, and evaluated their performance using metrics such as RMSE, MAE, SSE, SMAPE, global minimum ratio, and computation time. The results show that HNN2SATFuzzyMGWO outperformed the other hybrids, offering a more robust, accurate, and efficient solution to 2SAT problems. This work extends the applicability of HNN in solving SAT problems and provides a sophisticated alternative to classical Boolean approaches, paving the way for more adaptable problem-solving techniques in this field.