An Improved Transiently Chaotic Neural Network for Solving the K-Coloring Problem

Abstract

AbstractThis paper applies a new version of the transiently chaotic neural network (TCNN), the speedy convergent chaotic neural network (SCCNN), to solve the k-coloring problem, a classic NP-complete graph optimization problem, which has many real-world applications. From analyzing the chaotic states of its computational energy, we reach the conclusion that, like the TCNN, the SCCNN can avoid getting stuck in local minima and thus yield excellent solutions, which overcome the disadvantage of the Hopfield neural network (HNN). In addition, the experimental results verify that the SCCNN converges more quickly than the TCNN does in solving the k-coloring problem, which leads it to be a practical algorithm like the HNN. Therefore, the SCCNN not only adopts the advantages of the HNN as well as the TCNN but also avoids their drawbacks, thus provides an effective and efficient approach to solve the k-coloring problem.