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Graphical model construction based on evolutionary algorithms

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Abstract

Using Bayesian networks to model promising solutions from the current population of the evolutionary algorithms can ensure efficiency and intelligence search for the optimum. However, to construct a Bayesian network that fits a given dataset is a NP-hard problem, and it also needs consuming mass computational resources. This paper develops a methodology for constructing a graphical model based on Bayesian Dirichlet metric. Our approach is derived from a set of propositions and theorems by researching the local metric relationship of networks matching dataset. This paper presents the algorithm to construct a tree model from a set of potential solutions using above approach. This method is important not only for evolutionary algorithms based on graphical models, but also for machine learning and data mining. The experimental results show that the exact theoretical results and the approximations match very well.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Xidian University, Xi’an, Shannxi, 710071, China

    Youlong Yang, Yan Wu & Sanyang Liu

Authors
  1. Youlong Yang
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  2. Yan Wu
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  3. Sanyang Liu
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Additional information

This work was supported by the National Natural Science Foundation of China(No.60574075) and by Natural Science Foundation of Shaanxi Province(No.2005A07).

Youlong YANG received his B.S. and M.S. in Mathematics from Shaanxi Normal University, Xi’an, China in 1990 and 1993 respectively, and Ph.D. in System Engineering from Northwester Polytechnical University, Xi’an,China in 2003. Since 2004, he has been an associate professor at the School of Science, Xidian University, Xi’an,China. His research interests include Bayesian networks, intelligent optimization theory and evolutionary algorithms.

Yan WU received her B.S. in Mathematics from Shaanxi Normal University, Xi’an, Shaanxi Province of China in 1993. Since 2004, she has been a senior lecturer Faculty of Application Mathematics at the School of Science, Xidian University, Xi’an, Shaanxi Province of China. Her research interests include optimization theory and its application, evolutionary algorithms and graph model.

Sanyang LIU received his B.S. in Mathematics from Shaanxi Normal University, Xi’an, China in 1981, M.S. in Applied Mathematics from Xidian University, Xi’an, China in 1984, and Ph.D. in Computational Mathematics from Xi’an Jiaotong University, Xi’an, China in 1989. He is a professor and chairman of the School of Science, Xidian University. His research interests include modern analysis, optimization theory and algorithms.

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Yang, Y., Wu, Y. & Liu, S. Graphical model construction based on evolutionary algorithms. J. Control Theory Appl. 4, 349–354 (2006). https://doi.org/10.1007/s11768-006-5254-5

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  • DOI: https://doi.org/10.1007/s11768-006-5254-5

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