A Columnar Competitive Model with Simulated Annealing for Solving Combinatorial Optimization Problems

One of the major drawbacks of the Hopfield network is that when it is applied to certain polytopes of combinatorial problems, such as the traveling salesman problem (TSP), the obtained solutions are often invalid, requiring numerous trial-and-error setting of the network parameters thus resulting in low-computation efficiency. With this in mind, this article presents a columnar competitive model (CCM) which incorporates a winner-takes-all (WTA) learning rule for solving the TSP. Theoretical analysis for the convergence of the CCM shows that the competitive computational neural network guarantees the convergence of the network to valid states and avoids the tedious procedure of determining the penalty parameters. In addition, its intrinsic competitive learning mechanism enables a fast and effective evolving of the network. Simulation results illustrate that the competitive model offers more and better valid solutions as compared to the original Hopfield network.