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
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)
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)
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)
Cook, S.A.: The complexity of theorem proving procedures. In: 3rd Annual ACM Symposium on the Theory of Computing, pp. 151–158 (1971)
Cutchill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings 24th National of the ACM, pp. 157–172 (1969)
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)
Dueck, G., Jeffs, J.: A heuristic bandwidth reduction algorithm. Journal of combinatorial mathematics and computers (18), 97–108 (1995)
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)
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)
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)
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)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, Inc., Reading (1989)
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)
Gottlieb, J., Marchiori, E., Rossi, C.: Evolutionary algorithms for the satisfiability problem. Evolutionary Computation 10(1), 35–50 (2002)
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)
Haralambides, J., Makedon, F., Monien, B.: An aproximation algorithm for caterpillars. Journal of Mathematical Systems Theory 24, 169–177 (1991)
Harary, F.: Theory of graphs and its aplications, Czechoslovak Academy of Science, Prague (1967), M. Fiedler
Harper, L.H.: Optimal assignment of numbers to vertices. Journal of SIAM 12, 131–135 (1964)
Holland, J.: Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor (1975)
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)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)
Kosko, E.: Matrix inversion by partitioning - Part 2. The Aeronautical Quarterly (8), 157 (1956)
Livesley, R.R.: The analysis of large structural systems. Computer Journal 3(1), 34–39 (1960)
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)
Papadimitriou, C.H.: The NP-Completeness of the bandwidth minimization problem. Journal on Computing 16, 263–270 (1976)
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)
Mazure, B., Sais, L., Gregoire, E.: Tabu search for SAT. In: Proc. National Conference on Artificial Intelligence (AAAI-1997), pp. 281–285 (1997)
Smith, J.: On Appropriate Adaptation Levels for the Learning of Gene Linkage. Journal of Genetic Programming and Evolvable Machines 3, 129–155 (2002)
Spears, W.M.: Simulated Annealing for Hard Satisfiability Problems, Tech. Report AIC-93-015, AI Center, Naval Research Laboratory, Washington, DC 20375 (1993)
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)
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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
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