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.

[1]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[2]  Hidetomo Ichihashi,et al.  A simple steepest descent method for minimizing Hopfield energy to obtain optimal solution of the TSP with reasonable certainty , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[3]  Jzau-Sheng Lin,et al.  The application of competitive Hopfield neural network to medical image segmentation , 1996, IEEE Trans. Medical Imaging.

[4]  Pedro M. Talaván,et al.  Parameter setting of the Hopfield network applied to TSP , 2002, Neural Networks.

[5]  Mahesan Niranjan,et al.  A theoretical investigation into the performance of the Hopfield model , 1990, IEEE Trans. Neural Networks.

[6]  Satoshi Matsuda,et al.  "Optimal" Hopfield network for combinatorial optimization with linear cost function , 1998, IEEE Trans. Neural Networks.

[7]  George Papageorgiou,et al.  Improved exploration in Hopfield network state-space through parameter perturbation driven by simulated annealing , 1998, Eur. J. Oper. Res..

[8]  Kate Smith-Miles,et al.  Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research , 1999, INFORMS J. Comput..

[9]  Shigeo Abe.  Global convergence and suppression of spurious states of the Hopfield neural networks , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[10]  Mengkang Peng,et al.  An Investigation into the Improvement of Local Minima of the Hopfield Network , 1996, Neural Networks.

[11]  Pheng-Ann Heng,et al.  Winner-take-all discrete recurrent neural networks , 2000 .