A columnar competitive model for solving combinatorial optimization problems

The major drawbacks of the Hopfield network when it is applied to some combinatorial problems, e.g., the traveling salesman problem (TSP), are invalidity of the obtained solutions, trial-and-error setting value process of the network parameters and low-computation efficiency. This letter presents a columnar competitive model (CCM) which incorporates 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 to valid states and avoids the onerous procedures of determining the penalty parameters. In addition, its intrinsic competitive learning mechanism enables a fast and effective evolving of the network. The simulation results illustrate that the competitive model offers more and better valid solutions as compared to the original Hopfield network.