Neural network to solve fuzzy constraint satisfaction problems

Abstract

It has been proven that solving the constraint satisfaction problem (CSP) is an No Polynomial hard combinatorial optimization problem. This holds true even in cases where the constraints are fuzzy, known as fuzzy constraint satisfaction problems (FCSP). Therefore, the continuous Hopfield neural network model can be utilized to resolve it. The original algorithm was developed by Talaavan in 2005. Many practical problems can be represented as a FCSP. In this paper, we expand on a neural network technique that was initially developed for solving CSP and adapt it to tackle problems that involve at least one fuzzy constraint. To validate the enhanced effectiveness and rapid convergence of our proposed approach, a series of numerical experiments are carried out. The results of these experiments demonstrate the superior performance of the new method. Additionally, the experiments confirm its fast convergence. Specifically, our study focuses on binary instances with ordinary constraints to test the proposed resolution model. The results confirm that both the proposed approaches and the original continuous Hopfield neural network approach exhibit similar performance and robustness in solving ordinary constraint satisfaction problems.