Abstract
The investigation of genetic and evolutionary algorithms on Ising model problems gives much insight how these algorithms work as adaptation schemes. The Ising model on the ring has been considered as a typical example with a clear building block structure suited well for two-point crossover. It has been claimed that GAs based on recombination and appropriate diversity-preserving methods outperform by far EAs based only on mutation. Here, a rigorous analysis of the expected optimization time proves that mutation-based EAs are surprisingly effective. The (1+λ) EA with an appropriate λ-value is almost as efficient as usual GAs. Moreover, it is proved that specialized GAs do even better and this holds for two-point crossover as well as for one-point crossover.
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References
Culberson, J.: Genetic invariance: A new paradigm for genetic algorithm design. Technical Report 92–02, University of Alberta (1992)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addision-Wesley, Reading (1989)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan, MI (1975)
Ising, E.: Beiträge zur Theorie des Ferromagnetismus. Z. Physik (31), 235–258 (1925)
Jansen, T., De Jong, K.: An analysis of the role of offspring population size in EAs. In: Proc. of the Genetic and Evolutionary Computation Conference (GECCO 2002), San Mateo, CA, pp. 238–246. Morgan Kaufmann, San Francisco (2002)
Jansen, T., De Jong, K., Wegener, I.: On the choice of the offspring population size in evolutionary algorithms. Submitted to Evolutionary Computation (2003)
Naudts, B., Naudts, J.: The effect of spin-flip symmetry on the performance of the simple GA. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 67–76. Springer, Heidelberg (1998)
Pelikan, M., Goldberg, D.E.: Hierarchical BOA solves Ising spin glasses and MAXSAT. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1271–1282. Springer, Heidelberg (2003)
Van Hoyweghen, C.: Symmetry in the Representation of an Optimization Problem. PhD thesis, Univ. Antwerpen (2002)
Van Hoyweghen, C., Goldberg, D.E., Naudts, B.: Building block superiority, multimodality and synchronization problems. Technical report, Illinois Genetic Algorithms Laboratory, IlliGAL Rep. No. 2001020 (2001)
Van Hoyweghen, C., Goldberg, D.E., Naudts, B.: From twomax to the Ising model: Easy and hard symmetrical problems. In: Proc. of the Genetic and Evolutionary Computation Conference (GECCO 2002), San Mateo, CA, pp. 626–633. Morgan Kaufmann, San Francisco (2002)
Van Hoyweghen, C., Naudts, B., Goldberg, D.E.: Spin-flip symmetry and synchronization. Evolutionary Computation (10), 317–344 (2002)
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Fischer, S., Wegener, I. (2004). The Ising Model on the Ring: Mutation Versus Recombination. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24854-5_109
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DOI: https://doi.org/10.1007/978-3-540-24854-5_109
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