On the model updating operators in univariate estimation of distribution algorithms
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The role of the selection operation—that stochastically discriminate between individuals based on their merit—on the updating of the probability model in univariate estimation of distribution algorithms is investigated. Necessary conditions for an operator to model selection in such a way that it can be used directly for updating the probability model are postulated. A family of such operators that generalize current model updating mechanisms is proposed. A thorough theoretical analysis of these operators is presented, including a study on operator equivalence. A comprehensive set of examples is provided aiming at illustrating key concepts, main results, and their relevance.
KeywordsCompact genetic algorithm Estimation of distribution algorithms Selection operator Theoretical analysis
Andrey Bronevich is grateful to the Erasmus Mundus Triple I Consortium that supported a 10-months academic visit to the University of Algarve in 2010. This work is an outcome of a research cooperation between the authors that began with this visit. Andrey Bronevich also thanks the National Research University Higher School of Economics, Moscow, Russia for providing him with 1 month research grant for visiting University of Algarve in July 2014 facilitating the conclusion of the work. José Valente de Oliveira also thanks the National Research University Higher School of Economics, for inviting him for one week visit in November 2014.
- Baluja S (1994) Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Technical report CMU-CS-94-13. Carnegie Mellon University, Pittsburgh, Pennsylvania, USAGoogle Scholar
- Baluja S, Davies S (1997) Using optimal dependency-trees for combinatorial optimization: learning the structure of the search space. In: Proceedings of the 14-th International Conference on Machine Learning. San Francisco, California, USA, pp 30–38Google Scholar
- De Bonet JS, Isbell CL, Viola P (1997) MIMIC: finding optima by estimating probability densities. In: Petsche T, Mozer MC, Jordan MI (eds) Advances in neural information processing systems. MIT Press, Cambridge, pp 424–430Google Scholar
- Harik GR (1999) Linkage learning via probabilistic modeling in the ECGA. Technical report 99010. Illinois Genetic Algorithms Laboratory, University of Illinois, Urbana, Illinois, USAGoogle Scholar
- Johnson A, Shapiro JL (2002) The importance of selection mechanisms in distribution estimation algorithms. In: Collet P, Fonlupt C, Hao JK, Lutton E, Schoenauer M (ed) Evolution artificial, vol 2310. Lecture Notes in Computer Science, Springer, pp 91–103Google Scholar
- Mühlenbein H, Mahnig T (1998) Convergence theory and applications of the factorized distribution algorithm. J Comput Inf Technol 7:19–32Google Scholar
- Mühlenbein H, Mahnig T (2002) Evolutionary algorithms and the Boltzmann distribution. In: DeJong KA, Poli R, Rowe J (eds) Foundation of genetic algorithms 7. Morgan Kaufmann, Burlington, pp 133–150Google Scholar
- Pelikan M, Goldberg DE (2000) Genetic algorithms, clustering, and the breaking of symmetry. Lecture Notes in Computer Science 1917, pp 385–394Google Scholar
- Pelikan M, Goldberg DE (2001) Escaping hierarchical traps with competent genetic algorithms. In: Genetic and Evolutionary Computation Conference, pp 511–518Google Scholar
- Pelikan M, Mühlenbein H (1999) The bivariate marginal distribution algorithm. In: Chawdhry PK, Roy R, Furuhashi T (eds) Advances in soft computing—engineering design and manufacturing. Springer, Berlin, pp 521–535Google Scholar
- Sastry K, Goldberg DE (2001) Modeling tournament selection with replacement using apparent added noise. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001). San Francisco, California, USA, p 781Google Scholar