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International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming

CPAIOR 2012: Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems pp 66–80Cite as

Complete Characterization of Near-Optimal Sequences for the Two-Machine Flow Shop Scheduling Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7298))

Abstract

In a two-machine flow shop scheduling problem, the set of ε-approximate sequences (i.e., solutions within a factor 1 + ε of the optimal) can be mapped to the vertices of a permutation lattice.

We introduce two approaches, based on properties derived from the analysis of permutation lattices, for characterizing large sets of near-optimal solutions. In the first approach, we look for a sequence of minimum level in the lattice, since this solution is likely to cover many optimal or near-optimal solutions. In the second approach, we look for all sequences of minimal level, thus covering all ε-approximate sequences.

Integer linear programming and constraint programming models are first proposed to solve the former problem. For the latter problem, a direct exploration of the lattice, traversing it by a simple tree search procedure, is proposed. Computational experiments are given to evaluate these methods and to illustrate the interest and the limits of such approaches.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique, Université François-Rabelais Tours, 64 avenue Jean Portalis, 37200, Tours, France

    Jean-Charles Billaut

  2. CNRS, LAAS, 7 avenue du colonel Roche, 31077, Toulouse, France

    Emmanuel Hebrard & Pierre Lopez

  3. Université de Toulouse, UPS, INSA, INP, ISAE, UT1, UTM, LAAS, 31077, Toulouse, France

    Emmanuel Hebrard & Pierre Lopez

Authors
  1. Jean-Charles Billaut
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  2. Emmanuel Hebrard
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  3. Pierre Lopez
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Editor information

Editors and Affiliations

  1. École des Mines de Nantes, 4, rue Alfred Kastler, 44307, Nantes Cedex 3, France

    Nicolas Beldiceanu

  2. École des Mines de Nantes, 4 rue Alfred Kastler, 44307, Nantes Cedex 3, France

    Narendra Jussien

  3. Institut de Mathématiques Appliquées, 44 rue Rabelais, 49008, Angers Cedex 01, France

    Éric Pinson

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© 2012 Springer-Verlag Berlin Heidelberg

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Billaut, JC., Hebrard, E., Lopez, P. (2012). Complete Characterization of Near-Optimal Sequences for the Two-Machine Flow Shop Scheduling Problem. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds) Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol 7298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29828-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-29828-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29827-1

  • Online ISBN: 978-3-642-29828-8

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