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A Memetic Algorithm Guided by Quicksortfor the Error-Correcting Graph Isomorphism Problem

  • Rodolfo Torres-Velázquez
  • Vladimir Estivill-Castro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2279)

Abstract

Sorting algorithms define paths in the search space of n! permutations based on the information provided by a comparison predicate. We guide a Memetic Algorithm with a new mutation operator. Our mutation operator performs local search following the path traced by the Quicksort mechanism. The comparison predicate and the evaluation function are made to correspond and guide the evolutionary search. Our approach improves previous results for a benchmark of experiments of the Error-Correcting Graph Isomorphism. For this case study, our new Memetic Algorithm achieves a better quality vs effort trade-off and remains highly effective even when the size of the problem grows.

Keywords

Genetic Algorithm Local Search Mutation Operator Memetic Algorithm Sorting Algorithm 
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.

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References

  1. 1.
    Greffenstette, J.: Incorporating problem specific knowledge into genetic algorithms. Davis, L., ed.: Genetic Algorithms and Simulated Annealing, Pitman (1987) 42–60Google Scholar
  2. 2.
    Mühlenbein, H.: Parallel genetic algorithms, population genetics and combinatorial optimization. Schaffer, J., ed.: Proc. 3rd Int. Conf. Genetic Algorithms, George Mason Univ., Morgan Kaufmann (1989) 416–421Google Scholar
  3. 3.
    Davis, L., ed.: Handbook of Genetic Algorithms. Van Nostrand Reinhold (1991)Google Scholar
  4. 4.
    Mühlenbein, H.: Evolution in time and space-the parallel genetic algorithm. Rawlins, G., ed.: Foundations of Genetic Algorithms, Indiana Univ., Morgan Kaufmann (1991) 316–337Google Scholar
  5. 5.
    Merz, P., Freisleben, B.: A genetic local search approach to the quadratic assignment problem. Bäck, T., ed.: Proc. 7th Int. Conf. Genetic Algorithms, Michigan State Univ., East Lansing, Morgan Kaufmann (1997) 465–472Google Scholar
  6. 6.
    Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE T. Evolutionary Computation 4 (2000) 337–352CrossRefGoogle Scholar
  7. 7.
    Tsai, H.K., Yang, J.M., Kao, C.Y.: A genetic algorithm for traveling salesman problems. Spector, L., et al. eds.: GECCO-2001. Proc. Genetic and Evolutionary Conference, San Francisco, CA. Morgan Kaufmann (2001) 687–693Google Scholar
  8. 8.
    Rocha, M., Mendes, R., Cortez, P., Neves, J.: Sitting guests at a wedding party: Experiments on genetic and evolutionary constrained optimization. Congress on Evolutionary Computation CEC2001, Seoul, Korea, IEEE Press (2001) 671–678Google Scholar
  9. 9.
    Estivill-Castro, V., Torres-Velázquez, R.: Classical sorting embedded in genetic algorithms for improved permutation search. Congress on Evolutionary Computation CEC2001, Seoul, Korea, IEEE Press (2001) 941–948Google Scholar
  10. 10.
    Estivill-Castro, V., Torres-Velázquez, R.: How should feasibility be handled by genetic algorithms on constraint combinatorial optimization problems? the case of the valued n-queens problem. 2nd Workshop on Memetic Algorithms. WOMA II. GECCO-2001. (2001) 146–151Google Scholar
  11. 11.
    Wang, Y.K., Fan, K.C., Horng, J.T.: Genetic-based search for error-correcting graph isomorphism. IEEE T. Systems, Man and Cybernetics, Part B: Cybernetics 27 (1997) 588–597CrossRefGoogle Scholar
  12. 12.
    Tsai, W.H., Fu, K.S.: Error-correcting isomorphisms of attributed relational graphs for pattern analysis. IEEE T. Systems, Man and Cybernetics 9 (1979) 757–768zbMATHCrossRefGoogle Scholar
  13. 13.
    Messmer, B., Bunke, H.: A decision tree approach to graph and subgraph isomorphism detection. Pattern Recognition (1999) 1979–1998Google Scholar
  14. 14.
    Aarts, E., Lenstra, J.: Introduction. Aarts, E., Lenstra, J., eds.: Local Search in Combinatorial Optimization, Wiley (1997) 1–17Google Scholar
  15. 15.
    Knuth, D.: Sorting and Searching. Volume 3 of The Art of Computer Programming. Addison-Wesley (1973)Google Scholar
  16. 16.
    Sedgewick, R.: Algorithms in C++. Addison-Wesley (1992)Google Scholar
  17. 17.
    Estivill-Castro, V., Wood, D.: Randomized adaptive sorting. Random Structures and Algorithms 4 (1993) 26–51MathSciNetGoogle Scholar
  18. 18.
    Croes, G.: A method for solving traveling-salesman problems. Operations Research 5 (1958) 791–812MathSciNetCrossRefGoogle Scholar
  19. 19.
    Goldberg, D., Lingle, R.J.: Alleles, loci, and the traveling salesman problem. Grefenstette, J., ed.: Proc. Int. Conf. Genetic Algorithms and their Applications, Carnegie Mellon Univ., Lawrence Erlbaum (1985) 154–159Google Scholar
  20. 20.
    Baker, J.: Adaptive selection methods for genetic algorithms. Grefenstette, J., ed.: Proc. Int. Conf. on Genetic Algorithms and their Applications, Carnegie Mellon Univ., Lawrence Erlbaum (1985)Google Scholar
  21. 21.
    Wolpert, D.H., MacReady, W.: No free lunch theorems for optimization. IEEE T. on Evolutionary Computation 1 (1997) 67–82CrossRefGoogle Scholar
  22. 22.
    Reingold, E., Nievergelt, J., Deo, N.: Combinatorial Algorithms, Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ (1977)Google Scholar
  23. 23.
    Li, M., Vitanyi, P.: A theory of learning simple concepts under simple distributions and average case complexity for the universal distribution. Proc. 30th IEEE Symp. on Foundations of Computer Science, Research Triangle Park, NC. (1989) 34–39Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Rodolfo Torres-Velázquez
    • 1
  • Vladimir Estivill-Castro
    • 1
  1. 1.School of Electrical Engineering and Computer ScienceUniversity of NewcastleCallaghanAustralia

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