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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Greffenstette, J.: Incorporating problem specific knowledge into genetic algorithms. Davis, L., ed.: Genetic Algorithms and Simulated Annealing, Pitman (1987) 42–60
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) 416–421
Davis, L., ed.: Handbook of Genetic Algorithms. Van Nostrand Reinhold (1991)
Mühlenbein, H.: Evolution in time and space-the parallel genetic algorithm. Rawlins, G., ed.: Foundations of Genetic Algorithms, Indiana Univ., Morgan Kaufmann (1991) 316–337
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) 465–472
Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE T. Evolutionary Computation 4 (2000) 337–352
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) 687–693
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) 671–678
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) 941–948
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) 146–151
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) 588–597
Tsai, W.H., Fu, K.S.: Error-correcting isomorphisms of attributed relational graphs for pattern analysis. IEEE T. Systems, Man and Cybernetics 9 (1979) 757–768
Messmer, B., Bunke, H.: A decision tree approach to graph and subgraph isomorphism detection. Pattern Recognition (1999) 1979–1998
Aarts, E., Lenstra, J.: Introduction. Aarts, E., Lenstra, J., eds.: Local Search in Combinatorial Optimization, Wiley (1997) 1–17
Knuth, D.: Sorting and Searching. Volume 3 of The Art of Computer Programming. Addison-Wesley (1973)
Sedgewick, R.: Algorithms in C++. Addison-Wesley (1992)
Estivill-Castro, V., Wood, D.: Randomized adaptive sorting. Random Structures and Algorithms 4 (1993) 26–51
Croes, G.: A method for solving traveling-salesman problems. Operations Research 5 (1958) 791–812
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) 154–159
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)
Wolpert, D.H., MacReady, W.: No free lunch theorems for optimization. IEEE T. on Evolutionary Computation 1 (1997) 67–82
Reingold, E., Nievergelt, J., Deo, N.: Combinatorial Algorithms, Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ (1977)
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) 34–39
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Torres-Velázquez, R., Estivill-Castro, V. (2002). A Memetic Algorithm Guided by Quicksortfor the Error-Correcting Graph Isomorphism Problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds) Applications of Evolutionary Computing. EvoWorkshops 2002. Lecture Notes in Computer Science, vol 2279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46004-7_18
Download citation
DOI: https://doi.org/10.1007/3-540-46004-7_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43432-0
Online ISBN: 978-3-540-46004-6
eBook Packages: Springer Book Archive