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Optimization by estimation of distribution with DEUM framework based on Markov random fields

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Abstract

This paper presents a Markov random field (MRF) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model.

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Author information

Authors and Affiliations

  1. Intelligent Systems Research Center, British Telicom, Adastral Park, Ipswich, IP5 3RE, UK

    Siddhartha Shakya

  2. School of Computing, The Robert Gordon University, Aberdeen, AB25 1HG, UK

    John McCall

Authors
  1. Siddhartha Shakya
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  2. John McCall
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Correspondence to Siddhartha Shakya.

Additional information

Siddhartha K. Shakya received his B.E. and M.E. degree in computer engineering from the Vladimir State University. Russia, in 1998 and 1999 respectively, and M.Sc. degree in intelligent systems from the University of Sussex. UK in 2002. He received his Ph.D. degree in computer science from the Robert Gordon University, Aberdeen, UK in 2006. Currently, he is a research fellow at the Intelligent Systems Research Center within BT research. Ipswich, UK. Prior to joining BT, he was a research assistant in School of Computing at the Robert Gordon University.

His research interests include theoretical and practical aspects of optimisation algorithms, particularly, evolutionary algorithms and estimation of distribution algorithms, probabilistic graphical models and Markov random fields, graph-drawing algorithms, machine learning techniques, bio-informatics and operational research techniques, such as revenue management and dynamic pricing. He is a member of IEEE and ACM societies in computational intelligence.

John McCall studied Pure Mathematics at the University of Aberdeen, where he completed a Ph.D. on the Stable Homotopy of Lie Groups in 1991. Since then his research interests have evolved through modeling and optimization to evolutionary algorithms and, latterly, strong focus on EDAs. He is particularly interested in Markov random field models and their potential to improve heuristic search by modeling fitness from samples of evaluated solutions. He also has a strong and abiding interest in applications of evolutionary algorithms to medical treatment optimization, in particular cancer chemotherapy, and has published extensively in this area. Other interests include particle swarms, ant colonies and artificial immune systems.

McCall is currently a senior lecturer in computing at Robert Gordon University where he leads the Computational Intelligence Research Group.

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Shakya, S., McCall, J. Optimization by estimation of distribution with DEUM framework based on Markov random fields. Int J Automat Comput 4, 262–272 (2007). https://doi.org/10.1007/s11633-007-0262-6

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  • DOI: https://doi.org/10.1007/s11633-007-0262-6

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