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The Unconstrained Binary Quadratic Programming for the Sum Coloring Problem

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  • Sidi Mohamed Douiri
  • Souad Elbernoussi

Abstract

Several recent studies have shown the efficacy of unconstrained binary quadratic programming (UBQP) to model and solve many combinatorial problems. In this paper we are interested in the minimum sum coloring problem (MSCP), a new variant of the traditional graph coloring problem (GCP). We give a reformulation of the problem (MSCP) as an unconstrained binary quadratic binary programming, and we resolve it afterward by a genetic algorithms. The proposed algorithm is evaluated on the DIMACS challenge benchmarks and computational results show that the proposed UBQP model achieves highly competitive results, compared with 4 state-of-the-art algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:masjnl:v:6:y:2012:i:9:p:26
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    References listed on IDEAS

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    3. Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.
    4. 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.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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