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Improving the Performance of a Genetic Algorithm Using a Variable-Reordering Algorithm

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Genetic and Evolutionary Computation – GECCO 2004 (GECCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3103))

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Abstract

Genetic algorithms have been successfully applied to many difficult problems but there have been some disappointing results as well. In these cases the choice of the internal representation and genetic operators greatly conditions the result.

In this paper a GA and a reordering algorithm were used for solve SAT instances. The reordering algorithm produces a more suitable encoding for a GA that enables a GA performance improvement. The attained improvement relies on the building-block hypothesis, which states that a GA works well when short, low-order, highly-fit schemata (building blocks) recombine to form even more highly fit higher-order schemata. The reordering algorithm delivers a representation which has the most related bits (i.e. Boolean variables) in closer positions inside the chromosome.

The results of experimentation demonstrated that the proposed approach improves the performance of a simple GA in all the tests accomplished. These experiments also allow us to observe the relation among the internal representation, the genetic operators and the performance of a GA.

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References

  1. Kambayashi, Y., Cha, B., Iwama, K., Miyasaki, S.: Local search algorithms for partial maxsat. In: Proceedings of the AAAI 1997, July 27-31, pp. 263–268 (1997)

    Google Scholar 

  2. Blickle, T., Thiele, L.: A mathematical analysis of tournament selection. In: Proceedings of the Sixth ICGA, pp. 9–16. Morgan Kaufmann Publishers, San Francisco (1995)

    Google Scholar 

  3. Chinn, P.Z., Chvatalova, J., Dewdney, A.K., Gibbs, N.E.: The bandwidth problem for graphs and matrices - a survey. Journal of Graph Theory 6(3), 223–254 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cook, S.A.: The complexity of theorem proving procedures. In: 3rd Annual ACM Symposium on the Theory of Computing, pp. 151–158 (1971)

    Google Scholar 

  5. Cutchill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings 24th National of the ACM, pp. 157–172 (1969)

    Google Scholar 

  6. Davidor, Y.: Epistasis Variance: A Viewpont of GA-Hardness. In: Proceedings of the Second Foundations of Genetic Algorithms Workshop, pp. 23–35. Morgan Kaufmann, San Francisco (1991)

    Google Scholar 

  7. Dueck, G., Jeffs, J.: A heuristic bandwidth reduction algorithm. Journal of combinatorial mathematics and computers (18), 97–108 (1995)

    Google Scholar 

  8. Eiben, A.E., Van Der Hauw, J.K., Van Hemert, J.: Graph coloring with adaptative evolutionary algorithms. Journal of Heuristics 4(1), 25–46 (1998)

    Article  MATH  Google Scholar 

  9. Fleurent, C., Ferland, J.: Object-oriented implementation of heuristic search methods for graph coloring, maximum clique, and satisfiability. In: Second DIMACS Challenge, Special Issue, AMS, Providence, Rhode Island, pp. 619–652 (1996)

    Google Scholar 

  10. Garey, M.R., Graham, R.L., Johnson, D.S., Knuth, D.E.: Complexity results for bandwidth minimization. SIAM Journal of Applied Mathematics 34, 477–495 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gibbs, N.E., Poole, W.G., Stockmeyer, P.K.: An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM Journal on Numerical Analysis 13, 235–251 (1976)

    Article  MathSciNet  Google Scholar 

  12. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, Inc., Reading (1989)

    MATH  Google Scholar 

  13. Gottlieb, J., Voss, N.: Improving the performance of evolutionary algorithms for the satisfiability problem by refining functions. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 621–630. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Gottlieb, J., Marchiori, E., Rossi, C.: Evolutionary algorithms for the satisfiability problem. Evolutionary Computation 10(1), 35–50 (2002)

    Article  Google Scholar 

  15. Gurari, E.M., Sudborough, I.H.: Improved dynamic programming algorithms for bandwidth minimization and the min-cut linear arrangement problem. Journal of Algorithms 5, 531–546 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  16. Haralambides, J., Makedon, F., Monien, B.: An aproximation algorithm for caterpillars. Journal of Mathematical Systems Theory 24, 169–177 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  17. Harary, F.: Theory of graphs and its aplications, Czechoslovak Academy of Science, Prague (1967), M. Fiedler

    Google Scholar 

  18. Harper, L.H.: Optimal assignment of numbers to vertices. Journal of SIAM 12, 131–135 (1964)

    MATH  MathSciNet  Google Scholar 

  19. Holland, J.: Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  20. De Jong, K.A., Spears, W.M.: Using genetic algorithms to solve NP-complete problems. In: Proceedings of the Third ICGA, Fairfax, Virginia, pp. 124–132 (1989)

    Google Scholar 

  21. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  22. Kosko, E.: Matrix inversion by partitioning - Part 2. The Aeronautical Quarterly (8), 157 (1956)

    Google Scholar 

  23. Livesley, R.R.: The analysis of large structural systems. Computer Journal 3(1), 34–39 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  24. Marchiori, E., Rossi, C.: A flipping genetic algorithm for hard 3-SAT problems. In: Proceedings of Genetic and Evolutionary Computation Conference, San Francisco, California, pp. 393–400. Morgan Kaufmann, San Francisco (1999)

    Google Scholar 

  25. Papadimitriou, C.H.: The NP-Completeness of the bandwidth minimization problem. Journal on Computing 16, 263–270 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  26. Rana, S., Whitley, D.: Genetic algorithm behavior in the MAXSAT domain. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 785–794. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  27. Mazure, B., Sais, L., Gregoire, E.: Tabu search for SAT. In: Proc. National Conference on Artificial Intelligence (AAAI-1997), pp. 281–285 (1997)

    Google Scholar 

  28. Smith, J.: On Appropriate Adaptation Levels for the Learning of Gene Linkage. Journal of Genetic Programming and Evolvable Machines 3, 129–155 (2002)

    Article  MATH  Google Scholar 

  29. Spears, W.M.: Simulated Annealing for Hard Satisfiability Problems, Tech. Report AIC-93-015, AI Center, Naval Research Laboratory, Washington, DC 20375 (1993)

    Google Scholar 

  30. Torres-Jimenez, J., Rodriguez-Tello, E.: A new measure for the bandwidth minimization problem. In: Monard, M.C., Sichman, J.S. (eds.) SBIA 2000 and IBERAMIA 2000. LNCS (LNAI), vol. 1952, pp. 477–486. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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Rodriguez-Tello, E., Torres-Jimenez, J. (2004). Improving the Performance of a Genetic Algorithm Using a Variable-Reordering Algorithm. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_10

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  • DOI: https://doi.org/10.1007/978-3-540-24855-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22343-6

  • Online ISBN: 978-3-540-24855-2

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