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A Memetic Algorithm with Genetic Particle Swarm Optimization and Neural Network for Maximum Cut Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4688))

Abstract

In this paper, we incorporate a chaotic discrete Hopfield neural network (CDHNN), as a local search scheme, into a genetic particle swarm optimization (GPSO) and develop a memetic algorithm GPSO-CDHNN for the maximum cut problem. The proposed algorithm not only performs exploration by using the population-based evolutionary search ability of the GPSO, but also performs exploitation by using the CDHNN. Simulation results show that the proposed algorithm has superior ability for maximum cut problems.

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References

  1. Karp, R.M.: Reducibility Among Combinatorial Problems. In: Complexity of Computer Computations, pp. 85–104. Plenum, New York (1972)

    Google Scholar 

  2. Barahona, F., Grotschel, M., Junger, M., Reinelt, G.: A Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design. Operations Research 36(3), 493–513 (1988)

    MATH  Google Scholar 

  3. Chang, K., Du, D.: Efficient algorithm for the Layer Assignment Problem. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems CAD-6(1), 67–78 (1987)

    Article  Google Scholar 

  4. Bertoni, A., Campadelli, P., Grossi, G.: An Approximation Algorithm for the Maximum Cut Problem and Its Experimental Analysis. In: Proceedings of algorithms and experiments, Trento, Italy, pp. 137–143 (1998)

    Google Scholar 

  5. Goemans, M.X., Williamson, D.P.: Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. Journal of ACM 42(6), 1115–1145 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Helmberg, C., Rendl, F.: A Spectral Bundle Method for Semidefinite Programming. SIAM Journal on Optimization 10(3), 673–696 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Benson, S., Ye, Y., Zhang, X.: Solving Large Scale Sparse Semidefinite Programs for Combinatorial Optimization. SIAM Journal on Optimization 10(2), 443–461 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Choi, C., Ye, Y.: Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver. Working paper, Department of Management Science, University of Iowa, Iowa (2000)

    Google Scholar 

  9. Burer, S., Monteiro, R.D.C., Zhang, Y.: Rand-Two Relaxation Heuristics for Maximum Cut and Other Binary Quadratic Programs. Technical Report TR00-33, Department of Computational and Applied Mathematics, Rice University, Texas (2000)

    Google Scholar 

  10. Galán-Marín, G., Muñoz-Pérez, J.: Design and Analysis of Maximum Hopfield Networks. IEEE Trans. Neural Networks 12(2), 329–339 (2001)

    Article  Google Scholar 

  11. Galán-Marín, G., Mérida-Casermeiro, E., Muñoz-Pérez, J.: Modelling competitive Hopfield networks for the maximum clique problem. Computer & Operations Research 30(4), 603–624 (2003)

    Article  MATH  Google Scholar 

  12. Wang, J., Tang, Z., Cao, Q., Wang, R.: Optimal Competitive Hopfield Network with Stochastic Dynamics for Maximum Cut Problem. International Journal of Neural Systems 14(4), 257–265 (2004)

    Article  Google Scholar 

  13. Wu, L.Y., Zhang, X.S., Zhang, J.L.: Application of Discrete Hopfield-Type Neural Network for Max-Cut Problem. In: Proceedings of 8th International Conference on Neural Information Processing, pp. 1439–1444. Fudan University Press, Shanghai (2001)

    Google Scholar 

  14. Hopfield, J.J., Tank, D.W.: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proceedings of the National Academy of Sciences, USA 79(8) (1982)

    Google Scholar 

  15. Wang, J., Tang, Z.: An Improved Optimal Competitive Hopfield Network for Bipartite Subgraph Problems. Neurocomputing 61C, 413–419 (2004)

    Article  Google Scholar 

  16. Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948. Piscataway, NJ (1995)

    Google Scholar 

  17. Kennedy, J., Eberhart, R.C.: A Discrete Binary Version of the Particle Swarm Algorithm. In: Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, pp. 4104–4109. Piscatawary, NJ (1997)

    Google Scholar 

  18. Yin, P.Y.: Genetic Particle Swarm Optimization for Polygonal Approximation of Digital Curves. Pattern Recognition and Image Analysis 16(2), 223–233 (2006)

    Article  Google Scholar 

  19. Parsopoulos, K.E., Vrahatis, M.N.: Recent Approaches to Global Optimization Problems Through Particle Swarm Optimization. Natural Computing 1(2–3), 235–306 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhou, C.S., Chen, T.L.: Chaotic Annealing for Optimization. Physical Review E 55(3), 2580–2587 (1997)

    Article  Google Scholar 

  21. Hammer, P.L.: Some Network Flow Problems Solved with Pseudo-Boolean Programming. Operation research 13, 388–399 (1965)

    Article  MathSciNet  Google Scholar 

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Kang Li Minrui Fei George William Irwin Shiwei Ma

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© 2007 Springer-Verlag Berlin Heidelberg

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Wang, J. (2007). A Memetic Algorithm with Genetic Particle Swarm Optimization and Neural Network for Maximum Cut Problems. In: Li, K., Fei, M., Irwin, G.W., Ma, S. (eds) Bio-Inspired Computational Intelligence and Applications. LSMS 2007. Lecture Notes in Computer Science, vol 4688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74769-7_33

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  • DOI: https://doi.org/10.1007/978-3-540-74769-7_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74768-0

  • Online ISBN: 978-3-540-74769-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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