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Noisy Chaotic Neural Networks for Combinatorial Optimization

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Challenges for Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 63))

Summary

In this Chapter, we review the virtues and limitations of the Hopfield neural network for tackling NP-hard combinatorial optimization problems (COPs). Then we discuss two new neural network models based on the noisy chaotic neural network, and applied the two methods to solving two different NP-hard COPs in communication networks. The simulation results show that our methods are superior to previous methods in solution quality. We also point out several future challenges and possible directions in this domain.

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References

  1. E. Aarts and J. Korst. Simulated Annealing and Boltzmann Machines. John Wiley, Chichester, 1989.

    MATH  Google Scholar 

  2. K. Aihara, T. Takabe, and M. Toyoda. Chaotic neural networks. Physics Letters A, 144:333-340, 1990.

    Article  MathSciNet  Google Scholar 

  3. Mustafa K. Mehmet Ali and F. Kamoun. Neural networks for shortest path computation and routing in computer networks. IEEE Trans. on Neural Networks, 4:9, 1993.

    Article  Google Scholar 

  4. R.D. Brandt, Y. Wang, A.J. Laub, and S.K. Mitra. Alternative net-work for solving the travelling salesman problem and the list-matching problem. In Proceedings IEEE International Joint Conference on Neural Networks, volume 2, pages 333-340, 1988.

    Article  Google Scholar 

  5. L. Chen and K. Aihara. Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks, 8:915-930, 1995.

    Article  Google Scholar 

  6. L. Chen and K. Aihara. Global searching ability of chaotic neural net-works. IEEE Trans. Circuits and Systems - I: Fundamental Theory and Applications, 46(8):974-993, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  7. G.W. Davis. Sensitivity analysis in neural net solutions. IEEE Trans. on Systems, Man and Cybernetics, 19:1078-1082, 1989.

    Article  Google Scholar 

  8. D.E. Van den Bout and T.K. Miller. A traveling salesman objective function that works. In Proceedings IEEE International Joint Conference on Neural Networks, volume 2, pages 299-303, 1988.

    Article  Google Scholar 

  9. N. Funabiki and J. Kitamichi. A gradual neural network algorithm for broadcast scheduling problems in packet radio networks. IEICE Trans. Fundamentals, E82-A:815-824, 1999.

    Google Scholar 

  10. N. Funabiki and S. Nishikawa. A binary hopfield neural-network approach for satellite broadcast scheduling problems. IEEE Trans. on Neural Networks, 8:441-445, 1997.

    Article  Google Scholar 

  11. N. Funabiki and S. Nishikawa. A gradual neural-network approach for frequency assignment in satellite communication systems. IEEE Trans. Neural Networks, 8:1359-1370, 1997.

    Article  Google Scholar 

  12. V. Catania G. Ficili S. Palazzo G. Ascia and D. Panno. A VLSI fuzzy expert system for real-time tra.c control in atm networks. IEEE Transactions on Fuzzy Systems, 5(1):20-31, 1997.

    Article  Google Scholar 

  13. S. Geman and D. Geman. Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. Pattern Analysis and machine Intelligence, 6:721-741, 1984.

    Article  MATH  Google Scholar 

  14. Y. Hayakawa, Marunoto A, and Y. Sawada. Effects of the chaotic noise on the performance of a neural network model for optimization problems. Physical Review E, 51:2693-2696, 2002.

    Article  Google Scholar 

  15. S. Hegde, J. Sweet, and W. Levy. Determination of parameters in a hopfield/tank computational network. In Proceedings IEEE International Conference in Neural Networks, volume 2, pages 291-298, 1988.

    Google Scholar 

  16. J.J. Hopfield. Neurons with graded response have collective computa-tional properties like those of two-state neurons. In Proc. Natl. Acad. Sci. USA, volume 81, pages 3088-3092, 1984.

    Article  Google Scholar 

  17. J.J. Hopfield and D. W. Tank. Neural computation of decisions in opti-mization problems. Biological Cybernetics, 52:141-152, 1985.

    MATH  MathSciNet  Google Scholar 

  18. M. Jeruchim. A survey of interference problems and applications to geo-stationary satellite networks. In Proceedings IEEE, pages 317-331, 1977.

    Google Scholar 

  19. D.S. Johnson, C.H. Papadimitriou, and M. Yannakakis. Optimzation by simulated annealing: an experimental evalution, part 1, graph partitioning. Operat. Res., 37:865-892, 1989.

    Article  MATH  Google Scholar 

  20. D.S. Johnson, C.H. Papadimitriou, and M. Yannakakis. Optimzation by simulated annealing: an experimental evalution, part 2, graph partitioning. Operat. Res., 39:378-406, 1991.

    Article  MATH  Google Scholar 

  21. D. Jungnickel. Graphs, Netwrks and Algorithms. Springer-Verlag, Berlin,Germany, 1999.

    Google Scholar 

  22. B. Kamgar-Parsi and B. Kamgar-Parsi. Dynamical stability and parame-ter selection in neural optimization. In Proceedings IEEE International Joint Conference on Neural Networks, volume 4, pages 566-571, 1992.

    Google Scholar 

  23. S. Kirkpatrick, C.D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671-680, 1983.

    Article  MathSciNet  Google Scholar 

  24. T. Kwok and K.A. Smith. A noisy self-organizing neural network with bifurcation dynamics for combinatorial optimization. IEEE Trans. on Neural Networks, 15:84-98, 2004.

    Article  Google Scholar 

  25. W.K. Lai and G.G. Coghill. Genetic breeding of control parameters for the hopfield/tank neural net. In Proceedings IEEE International Joint Conference on Neural Networks, volume 4, pages 618-632, 1992.

    Google Scholar 

  26. O. Lazaro and D. Girma. A hopfield neural-network-based dynamic chan-nel allocation with handoff channel reservation control. IEEE Trans. on Vehicular Technology, 49:1578-1687, 2000.

    Article  Google Scholar 

  27. R.S.T. Lee. A transient-chaotic autoassociative network (tcan) based on lee oscillators. IEEE Trans. on Neural Networks, 15:1228-1243, 2004.

    Article  Google Scholar 

  28. T. Mizuike and Y. Ito. Optimization of frequency assignment. IEEE Trans. Communications, 37:1031-1041, 1989.

    Article  Google Scholar 

  29. H. Nonaka and Y. Kobayashi. Sub-optimal solution screening in opti-mization by neural networks. In Proceedings IEEE International Joint Conference on Neural Networks, volume 4, pages 606-611, 1992.

    Google Scholar 

  30. H. Nozawa. A neural network model as a globally coupled map and applications based on chaos. Chaos, 2(3):377-386, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  31. B. Pontano. Interference into angel-modulated systems carrying multi-channel telephony signals. IEEE Trans. Communications, 21, 1973.

    Google Scholar 

  32. C.R. Reeves. Modern Heuristic Techniques for Combinatorial Problems. Oxford, Blackwell, 1993.

    MATH  Google Scholar 

  33. S. Salcedo-Sanz, C. Bouso no Calzón, and A.R. Figueiras-Vidal. A mixed neural-genetic algorithm for the broadcast scheduling problem. IEEE Trans. on Wireless communications, 2:277-283, 2003.

    Article  Google Scholar 

  34. S. Salcedo-Sanz, R. Santiago-Mozos, and C. Bouso no Calzón. A hybrid hopfield network-simulated annealing approach for frequency assignment in satellite communications systems. IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics, 34:1108-1116, 2004.

    Article  Google Scholar 

  35. H.X. Shi and L.P. Wang. Broadcast scheduling in wireless multihop net-works using a neural-network-based hybrid algorithm. Neural Networks, 18:765C771, 2005.

    Google Scholar 

  36. H. Tang, K.C. Tan, and Z. Yi. A columnar competitive model for solving combinatorial optimization problems. IEEE Trans. on Neural Networks, 15:1568-1573, 2004.

    Article  Google Scholar 

  37. I. Tokuda, K. Aihara, and T. Nagashima. Adaptive annealing for chaotic optimization. Phys. Rev. E, 58:5157-5160, 1998.

    Article  MathSciNet  Google Scholar 

  38. A. Varma and Jayadeva. A novel digital neural network for the travelling salesman problem. In Neural Information Processing, 2002. ICONIP ’02, volume 2, pages 1320-1324, 2002.

    Google Scholar 

  39. G. Wang and N. Ansari. Optimal broadcast scheduling in packet radio networks using mean field annealing. IEEE Journal on Selected Areas in Communications, 15:250-260, 1997.

    Article  Google Scholar 

  40. L.P. Wang and F. Tian. Noisy chaotic neural networks for solving combi-natorial optimization problems. In Proc. International Joint Conference on Neural Networks, volume 4, pages 37-40, 2000.

    Google Scholar 

  41. L.P. Wang and K. Smith. On chaotic simulated annealing. IEEE Trans-actions on Neural Networks, 9:716-718, 1998.

    Article  Google Scholar 

  42. R.L. Wang, Z. Tang, and Q.P. Cao. A hopfield network learning method for bipartite subgraph problem. IEEE Trans. on Neural Networks, 15:1458-1465, 2004.

    Article  Google Scholar 

  43. G.V. Wilson and G.S. Pawley. On the stalibility of the travelling salesman problem algorithm of hopfield and tank. Biol. Cybern., 58:63-70, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  44. David H. Wolpert and William G. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1:67C82, 1997.

    Article  Google Scholar 

  45. M. Yamaguti, editor. Solution of the optimization problem using the neural network model as a globally coupled map, 1994.

    Google Scholar 

  46. M. Yamguti, editor. Transient chaotic neural networks and chaotic sim-ulated annealing. Amsterdam: Elsevier Science Publishers, 1994.

    Google Scholar 

  47. L. Zheng, K. Wang, and K. Tian. An approach to improve wang-smith chaotic simulated annealing. International Journal of Neural Systems, 12:363-368, 2002.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, 639798, Nanyang Avenue, Singapore

    Dr. Lipo Wang

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, 639798, Nanyang Avenue, Singapore

    Haixiang Shi

Authors
  1. Dr. Lipo Wang
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  2. Haixiang Shi
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Editor information

Editors and Affiliations

  1. Department of Informatics, Nicolaus Copernicus University, Ul. Grudziadzka 5, 87-100, Torun, Poland

    Włodzisław Duch

  2. Division of Computer Science, School of Computer Engineering, Nanyang Technological University, 639798, Singapore

    Włodzisław Duch

  3. Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland

    Jacek Mańdziuk

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© 2007 Springer-Verlag Berlin Heidelberg

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Wang, L., Shi, H. (2007). Noisy Chaotic Neural Networks for Combinatorial Optimization. In: Duch, W., Mańdziuk, J. (eds) Challenges for Computational Intelligence. Studies in Computational Intelligence, vol 63. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71984-7_17

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  • DOI: https://doi.org/10.1007/978-3-540-71984-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71983-0

  • Online ISBN: 978-3-540-71984-7

  • eBook Packages: EngineeringEngineering (R0)

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