Rigorous time complexity analysis of Univariate Marginal Distribution Algorithm with margins

Univariate Marginal Distribution Algorithms (UMDAs) are a kind of Estimation of Distribution Algorithms (EDAs) which do not consider the dependencies among the variables. In this paper, on the basis of our proposed approach in [1], we present a rigorous proof for the result that the UMDA with margins (in [1] we merely showed the effectiveness of margins) cannot find the global optimum of the TRAPLEADINGONES problem [2] within polynomial number of generations with a probability that is super-polynomially close to 1. Such a theoretical result is significant in sheding light on the fundamental issues of what problem characteristics make an EDA hard/easy and when an EDA is expected to perform well/poorly for a given problem.

[1]  Yang Yu,et al.  A new approach to estimating the expected first hitting time of evolutionary algorithms , 2006, Artif. Intell..

[2]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[3]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[4]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[5]  María Cristina González Morgado.  Contributions on theoretical aspects of estimation of distributions algorithms , 2006 .

[6]  Xin Yao,et al.  Analysis of Computational Time of Simple Estimation of Distribution Algorithms , 2010, IEEE Transactions on Evolutionary Computation.

[7]  R. Serfling.  Probability Inequalities for the Sum in Sampling without Replacement , 1974 .

[8]  XI FachbereichInformatik.  Finite Markov Chain Results in Evolutionary Computation: a Tour D'horizon , 1998 .

[9]  Per Kristian Lehre,et al.  When is an estimation of distribution algorithm better than an evolutionary algorithm? , 2009, 2009 IEEE Congress on Evolutionary Computation.

[10]  Xin Yao,et al.  Towards an analytic framework for analysing the computation time of evolutionary algorithms , 2003, Artif. Intell..

[11]  Stefan Droste,et al.  A rigorous analysis of the compact genetic algorithm for linear functions , 2006, Natural Computing.

[12]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[13]  David E. Goldberg,et al.  The compact genetic algorithm , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[14]  D. Goldberg,et al.  Domino convergence, drift, and the temporal-salience structure of problems , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[15]  Xin Yao,et al.  Drift analysis and average time complexity of evolutionary algorithms , 2001, Artif. Intell..

[16]  Xin Yao,et al.  On the analysis of average time complexity of estimation of distribution algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.