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A note on xQx as a modelling and solution framework for the Linear Ordering Problem

Author

Listed:
  • Mark Lewis
  • Bahram Alidaee
  • Fred Glover
  • Gary Kochenberger

Abstract

This paper expands the list of 0-1 problems that can be effectively modelled and solved as Unconstrained Quadratic Binary Programs (UQPs). UQP has been presented as a general-purpose modelling approach with application to a broad range of problem classes (Kochenberger et al., 2004). In this paper, we demonstrate that the Linear Ordering Problem (LOP) can be easily recast so that it can be treated as a UQP problem, and that large instances of the LOP can be effectively handled within this framework. Computational results are given demonstrating the viability and attractiveness of this approach.

Suggested Citation

  • Mark Lewis & Bahram Alidaee & Fred Glover & Gary Kochenberger, 2009. "A note on xQx as a modelling and solution framework for the Linear Ordering Problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(2), pages 152-162.
    • Handle: RePEc:ids:ijores:v:5:y:2009:i:2:p:152-162
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    Citations

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    Cited by:

    1. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    2. Christoph Buchheim & Angelika Wiegele & Lanbo Zheng, 2010. "Exact Algorithms for the Quadratic Linear Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 168-177, February.
    3. Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2010. "A hybrid metaheuristic approach to solving the UBQP problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1254-1262, December.
    4. Sidi Mohamed Douiri & Souad Elbernoussi, 2012. "The Unconstrained Binary Quadratic Programming for the Sum Coloring Problem," Modern Applied Science, Canadian Center of Science and Education, vol. 6(9), pages 1-26, September.

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