Juergen Branke
Clemens Lode
ABSTRACT
Estimation of distribution algorithms replace the typical crossover and mutation operators by constructing a probabilistic model and generating offspring according to this model. In previous studies, it has been shown that this generally leads to diversity loss due to sampling errors. In this paper, for the case of the simple Univariate Marginal Distribution Algorithm (UMDA), we propose and test several methods for counteracting diversity loss. The diversity loss can come in two phases: sampling from the probability model (offspring generation) and selection. We show that it is possible to completely remove the sampling error during offspring generation. Furthermore, we examine several plausible model construction variants which counteract diversity loss during selection and demonstrate that these update rules work better than the standard update on a variety of simple test problems.
- J. E. Baker. Reducing bias and inefficiency in the selection algorithm. In J. Grefenstette, editor, International Conference on Genetic Algorithms, pages 14--21. Lawrence Erlbaum Associates, 1987. Google Scholar
Digital Library
- S. Baluja and S. Davies. Using optimal dependency-trees for combinatorial optimization: Learing the structure of the search space. In D. Fisher, editor, International Conference on Machine Learning, pages 30--38, 1997. Google ScholarDigital Library
- J. Branke, M. Cutaia, and H. Dold. Reducing genetic drift in steady state evolutionary algorithms. In Wolfgang Banzhaf et al., editors, Genetic and Evolutionary Computation Conference, pages 68--74. Morgan Kaufmann, 1999.Google Scholar
- C. Gonzalez, J. Lozano, and P. LarraÜnaga. Analyzing the population based incremental learning algorithm by means of discrete dynamical systems. Complex Systems, 12(4):465--479, 2001.Google Scholar
- C. Gonzalez, J. Lozano, and P. LarraÜnaga. The convergence behaviour of the PBIL algorithm: a preliminary approach. In International Conference on Neural Networks and Genetic Algorithms, pages 228--231, 2001.Google ScholarCross Ref
- P. LarraÜnaga and J. A. Lozano. Estimation of Distribution Algorithms, A New Tool for Evolutionary Computation. Kluwer Academic Publishers, 2002.Google Scholar
- T. Mahnig and H. Mühlenbein. Optimal mutation rate using bayesian priors for estimation of distribution algorithms. In Stochastic Algorithms: Foundations and Applications, volume 2264 of LNCS, 2001. Google ScholarDigital Library
- H. Mühlenbein and G. Paaß. From recombination of genes to the estimation of distributions i: Binary parameters. In Parallel Problem Solving from Nature, pages 178--187, 1999. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- J. L. Shapiro. Scaling of probability-based optimization algorithms. In Klaus Obermayer, editor, Advances in Neural Information Processing Systems 15, pages 399--406. MIT Press, 2003.Google Scholar
- J. L. Shapiro. The detailed balance principle in estimation of distribution algorhithm. Evolutionary Computation, 13(1):99--124, 2005. Google ScholarDigital Library
- J. L. Shapiro. Diversity loss in general estimation of distribution algorithms. In Parallel Problem Solving from Nature, volume 4193 of LNCS, pages 92--101. Springer, 2006. Google ScholarDigital Library
- H. Wu and J. L. Shapiro. Does overfitting affect performance in estimation of distribution algorithms. In Genetic and Evolutionary Computation Conference, pages 433--434. ACM, 2006. Google ScholarDigital Library
Index Terms
- Addressing sampling errors and diversity loss in UMDA
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