Summary
This chapter presents an entropy-based convergence measurement applicable to Estimation of Distribution Algorithms. Based on the measured entropy, the time point when the generation of new solutions becomes ineffective, can be detected. The proposed termination criterion is inherent to the complexity of used probabilistic models and automatically postpones the termination if inappropriate models are used.
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References
D. M. Chickering, D. Geiger, and D. Heckerman. Learning Bayesian networks is NP-hard. Technical report, Microsoft Research, Redmond, WA, 1994.
D. M. Chickering, D. Heckerman, and C. Meek. A Bayesian approach to learning Bayesian networks with local structure. In Proceedings of Thirteenth Conference on Uncertainty in Artificial Intelligence, pp. 80–89. Morgan Kaufmann, 1997.
R. Etxeberria and P. Larrañaga. Global optimization with Bayesian networks. In II Symposium on Artificial Intelligence. CIMAF99. Special Session on Distributions and Evolutionary Optimization, pp. 332–339, 1999.
G. Harik. Finding multimodal solutions using restricted tournament selection. In Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA 6), pp. 24–31. Morgan Kaufmann, 1995.
D. Heckerman, D. Geiger, and D. M. Chickering. Learning Bayesian networks: The combination of knowledge and statistical data. Technical report, Microsoft Research, Redmond, WA, 1994.
P. Larrañaga. A review on estimation of distribution algorithms. In P. Larrañaga and J. A. Lozano, editors, Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation, pp. 80–90. Kluwer Academic Publishers, 2002.
H. Mühlenbein and T. Mahnig. FDA — a scalable evolutionary algorithm for the optimization of additively decomposed functions. Evolutionary Computation, 7(4):353–376, 1999.
H. Mühlenbein and G. Paaß. From recombination of genes to the estimation of distributions I. Binary parameters. In Lecture Notes in Computer Science 1411: Parallel Problem Solving from Nature-PPSN IV, pp. 178–187, 1996.
J. Ocenasek and J. Schwarz. Estimation of distribution algorithm for mixed continuous-discrete optimization problems. In IOS Press, editor, 2nd Euro-International Symposium on Computational Intelligence, pp. 227–232, 2002.
M. Pelikan, D. E. Goldberg, and E. Cantú-Paz. BOA: The Bayesian optimization algorithm. In W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith, editors, Proceedings of the Genetic and Evolutionary Computation Conference GECCO-99, volume 1, pp. 525–532. Morgan Kaufmann Publishers, San Francisco, CA, 1999. Orlando, FL.
M. Pelikan, D. E. Goldberg, and F. Lobo. A survey of optimization by building and using probabilistic models. Computational Optimization and Applications, 21(1):5–20, 2002.
M. Pelikan, D. E. Goldberg, and K. Sastry. Bayesian optimization algorithm, decision graphs, and Occam’s razor. In Proceedings of the Genetic and Evolutionary Computation Conference GECCO-2001, pp. 519–526. Morgan Kaufman, 2000.
M. Pelikan, J. Ocenasek, S. Trebst, M. Troyer, and F. Alet. Computational complexity and simulation of rare events of ising spin glasses. In Proceedings of the Genetic and Evolutionary Computation Conference GECCO-2004, pp. 36–47. Springer-Verlag, 2004.
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Ocenasek, J. (2006). Entropy-based Convergence Measurement in Discrete Estimation of Distribution Algorithms. In: Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds) Towards a New Evolutionary Computation. Studies in Fuzziness and Soft Computing, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32494-1_2
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DOI: https://doi.org/10.1007/3-540-32494-1_2
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