Optimizing Quadratic Satisfiability with Special Symbolic Logic in a Discrete Hopfield Neural Network Using Swarm Intelligence

Abstract

Conventional second-order logic satisfiability with Discrete Hopfield Neural Network has major drawbacks in obtaining potential solutions. This causes problems in a network because suboptimal final neuron states will affect any optimization problems. To overcome such issues, special types of symbolic logic, such as Fuzzy logic, can be impactful, which has emerged as a valuable tool for various applications, including engineering system control and neural networks. In this article, the authors propose a novel hybrid model that combines fuzzy logic with a satisfiability-based discrete Hopfield neural network and a swarm-type metaheuristic algorithm. The proposed method ensembles Fuzzy logic with Quadratic Satisfiability to construct the bipolar structure, while the Artificial Bee Colony algorithm, a swarm-based optimization technique, is applied to optimize the solution. The hybrid model is benchmarked against the existing second-order satisfiability-based Discrete Hopfield Neural Networks and conventional Fuzzy logic-based Discrete Hopfield Neural Networks. Simulation results show that the proposed hybrid model outperforms existing models by 85%-95% in terms of training-testing error analysis, energy efficiency, neuron variation, and computational time.