Maximum Neural Network with Nonlinear Self-Feedback and Its Application to Maximum Independent Set Problem

In this paper, based on the maximum neural network, we propose a new parallel algorithm that can escape from local minima and has powerful ability of searching the globally optimal or near-optimum solution for the maximum independent set problem (MISP). Given a graph, the aim of the MISP is to find the largest set of vertices such that no two vertices in the set are connected by an edge. The MISP is a classic optimization problem in computer science and in graph theory with many real-world applications, and is also known to be NP-complete. By adding a nonlinear self-feedback to the maximum neural network, we proposed a parallel algorithm that introduces richer and more flexible nonlinear dynamics and can prevent the network from getting stuck at local minima. After the nonlinear dynamics has vanished, the proposed algorithm then is fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. A large number of instances have been simulated to verify the proposed algorithm.