Rigorous time complexity analysis of univariate marginal distribution algorithm with margins

Authors:
Tianshi Chen;Ke Tang;Guoliang Chen;Xin Yao
Affiliations:
Nature Inspired Computation and Applications Laboratory, Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China;Nature Inspired Computation and Applications Laboratory, Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China;Nature Inspired Computation and Applications Laboratory, Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China;Nature Inspired Computation and Appl. Lab., Dept. of Comp. Sci. and Techn., Univ. of Sci. and Techn. of China, Hefei, Anhui, China and Centre of Excellence for Res. in Computational Intelligence a ...
Venue:
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Year:
2009

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Abstract

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.