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On the convergence of a factorized distribution algorithm with truncation selection

COMPLEXITY 2004年第4期9卷 17-23页

作者： Zhang, QF Univ Essex Dept Comp Colchester CO4 3SQ Essex England

We investigate the global convergence of a factorized distribution algorithm (FDA) with truncation selection. Like conventional genetic algorithms, FDAs maintain and successively improve a population of solutions. In FDAs a distribution model is built based on the statistical information extracted from a set of selected solutions in the current population, and then the model thus built is used to generate new solutions for the next generation. The variable-dependence structure of the distribution model in FDAs is determined by the variable-interaction structure of the objective function. We prove that the FDA with truncation selection converges globally for optimization of a class of additively decomposable functions (ADF). Our results imply that the utilization of appropriately selected dependence relationships is sufficient to guarantee the global convergence of estimation of distribution algorithms (EDAs) for optimization of ADFs. (c) 2004 Wiley Periodicals, Inc.

关键词： genetic algorithms estimation of distribution algorithms factorized distribution algorithms convergence infinite population

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Learning Factorizations in Estimation of distribution algorithms Using Affinity Propagation

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EVOLUTIONARY COMPUTATION 2010年第4期18卷 515-546页

作者： Santana, Roberto Larranaga, Pedro Lozano, Jose A. Univ Politecn Madrid Fac Informat E-28660 Madrid Spain Univ Politecn Madrid Dept Inteligencia Artificial E-28660 Madrid Spain Univ Basque Country Intelligent Syst Grp Dept Comp Sci & Artificial Intelligence San Sebastian 20018 Spain

Estimation of distribution algorithms (EDAs) that use marginal product model factorizations have been widely applied to a broad range of mainly binary optimization problems. In this paper, we introduce the affinity propagation EDA (AffEDA) which learns a marginal product model by clustering a matrix of mutual information learned from the data using a very efficient message-passing algorithm known as affinity propagation. The introduced algorithm is tested on a set of binary and nonbinary decomposable functions and using a hard combinatorial class of problem known as the HP protein model. The results show that the algorithm is a very efficient alternative to other EDAs that use marginal product model factorizations such as the extended compact genetic algorithm (ECGA) and improves the quality of the results achieved by ECGA when the cardinality of the variables is increased.

关键词： Estimation of distribution algorithms affinity propagation factorized distribution algorithms message-passing algorithms marginal product models factorizations extended compact genetic algorithm

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Estimation of distribution algorithms with Kikuchi approximations

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EVOLUTIONARY COMPUTATION 2005年第1期13卷 67-97页

作者： Santana, R Inst Cybernet Math & Phys Havana Cuba

The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of distribution algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables.

关键词： estimation of distribution algorithms factorized distribution algorithms Kikuchi approximations factorizations graphical models

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