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Graph-Based Local Elimination Algorithms in Discrete Optimization

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Foundations of Computational Intelligence Volume 3

Part of the book series: Studies in Computational Intelligence ((SCI,volume 203))

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Abstract

The aim of this chapter is to provide a review of structural decomposition methods in discrete optimization and to give a unified framework in the form of local elimination algorithms (LEA). This chapter is organized as follows. Local elimination algorithms for discrete optimization (DO) problems (DOPs) with constraints are considered; a classification of dynamic programming computational procedures is given. We introduce Elimination Game and Elimination tree. Application of bucket elimination algorithm from constraint satisfaction (CS) to solving DOPs is done. We consider different local elimination schemes and related notions. Clustering that merges several variables into single meta-variable defines a promising approach to solve DOPs. This allows to create a quotient (condensed) graph and apply a local block elimination algorithm. In order to describe a block elimination process, we introduce Block Elimination Game. We discuss the connection of aforementioned local elimination algorithmic schemes and a way of transforming the directed acyclic graph (DAG) of computational LEA procedure to the tree decomposition.

Research supported by FWF (Austrian Science Funds) under the project P17948-N13.

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  1. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090, Vienna, Austria

    Oleg Shcherbina

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  1. Oleg Shcherbina
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  1. Machine Intelligence Research Labs (MIR Labs), Scientific Network for Innovation and Research Excellence, P.O. Box 2259, 98071-2259, Auburn, Washington, USA

    Ajith Abraham

  2. College of Business Administration Quantitative and Information System Department, Kuwait University, P.O. Box 5486, 13055, Safat, Kuwait

    Aboul-Ella Hassanien

  3. Université Paris XII Fac. Sciences, LERISS, 61 avenue du Général de Gaulle Building P2 - Room 350, 94010, Créteil, France

    Patrick Siarry

  4. Department of Computer Science, University of Pretoria, 0002, Pretoria, South Africa

    Andries Engelbrecht

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Shcherbina, O. (2009). Graph-Based Local Elimination Algorithms in Discrete Optimization. In: Abraham, A., Hassanien, AE., Siarry, P., Engelbrecht, A. (eds) Foundations of Computational Intelligence Volume 3. Studies in Computational Intelligence, vol 203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01085-9_8

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