Advertisement

Noisy Chaotic Neural Networks for Combinatorial Optimization

  • Lipo Wang
  • Haixiang Shi
Part of the Studies in Computational Intelligence book series (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.

Keywords

Neural Network Time Slot Variable Threshold Frequency Assignment Chaotic Neural Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. Aarts and J. Korst. Simulated Annealing and Boltzmann Machines. John Wiley, Chichester, 1989. zbMATHGoogle Scholar
  2. [2]
    K. Aihara, T. Takabe, and M. Toyoda. Chaotic neural networks. Physics Letters A, 144:333-340, 1990. CrossRefMathSciNetGoogle Scholar
  3. [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. CrossRefGoogle Scholar
  4. [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. CrossRefGoogle Scholar
  5. [5]
    L. Chen and K. Aihara. Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks, 8:915-930, 1995. CrossRefGoogle Scholar
  6. [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. zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    G.W. Davis. Sensitivity analysis in neural net solutions. IEEE Trans. on Systems, Man and Cybernetics, 19:1078-1082, 1989. CrossRefGoogle Scholar
  8. [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. CrossRefGoogle Scholar
  9. [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. [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. CrossRefGoogle Scholar
  11. [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. CrossRefGoogle Scholar
  12. [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. CrossRefGoogle Scholar
  13. [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. zbMATHCrossRefGoogle Scholar
  14. [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. CrossRefGoogle Scholar
  15. [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. [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. CrossRefGoogle Scholar
  17. [17]
    J.J. Hopfield and D. W. Tank. Neural computation of decisions in opti-mization problems. Biological Cybernetics, 52:141-152, 1985. zbMATHMathSciNetGoogle Scholar
  18. [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. [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. zbMATHCrossRefGoogle Scholar
  20. [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. zbMATHCrossRefGoogle Scholar
  21. [21]
    D. Jungnickel. Graphs, Netwrks and Algorithms. Springer-Verlag, Berlin,Germany, 1999.Google Scholar
  22. [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. [23]
    S. Kirkpatrick, C.D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671-680, 1983. CrossRefMathSciNetGoogle Scholar
  24. [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. CrossRefGoogle Scholar
  25. [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. [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. CrossRefGoogle Scholar
  27. [27]
    R.S.T. Lee. A transient-chaotic autoassociative network (tcan) based on lee oscillators. IEEE Trans. on Neural Networks, 15:1228-1243, 2004. CrossRefGoogle Scholar
  28. [28]
    T. Mizuike and Y. Ito. Optimization of frequency assignment. IEEE Trans. Communications, 37:1031-1041, 1989. CrossRefGoogle Scholar
  29. [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. [30]
    H. Nozawa. A neural network model as a globally coupled map and applications based on chaos. Chaos, 2(3):377-386, 1992. zbMATHCrossRefMathSciNetGoogle Scholar
  31. [31]
    B. Pontano. Interference into angel-modulated systems carrying multi-channel telephony signals. IEEE Trans. Communications, 21, 1973. Google Scholar
  32. [32]
    C.R. Reeves. Modern Heuristic Techniques for Combinatorial Problems. Oxford, Blackwell, 1993. zbMATHGoogle Scholar
  33. [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. CrossRefGoogle Scholar
  34. [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. CrossRefGoogle Scholar
  35. [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. [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. CrossRefGoogle Scholar
  37. [37]
    I. Tokuda, K. Aihara, and T. Nagashima. Adaptive annealing for chaotic optimization. Phys. Rev. E, 58:5157-5160, 1998. CrossRefMathSciNetGoogle Scholar
  38. [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. [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. CrossRefGoogle Scholar
  40. [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. [41]
    L.P. Wang and K. Smith. On chaotic simulated annealing. IEEE Trans-actions on Neural Networks, 9:716-718, 1998. CrossRefGoogle Scholar
  42. [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. CrossRefGoogle Scholar
  43. [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. zbMATHCrossRefMathSciNetGoogle Scholar
  44. [44]
    David H. Wolpert and William G. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1:67C82, 1997. CrossRefGoogle Scholar
  45. [45]
    M. Yamaguti, editor. Solution of the optimization problem using the neural network model as a globally coupled map, 1994.Google Scholar
  46. [46]
    M. Yamguti, editor. Transient chaotic neural networks and chaotic sim-ulated annealing. Amsterdam: Elsevier Science Publishers, 1994.Google Scholar
  47. [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.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Lipo Wang
    • 1
  • Haixiang Shi
    • 2
  1. 1.School of Electrical and Electronic EngineeringNanyang Technological UniversityNanyang AvenueSingapore
  2. 2.School of Electrical and Electronic EngineeringNanyang Technological UniversityNanyang AvenueSingapore

Personalised recommendations