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A global optimization algorithm for solving the minimum multiple ratio spanning tree problem

Author

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  • Oleksii Ursulenko
  • Sergiy Butenko
  • Oleg Prokopyev

Abstract

This paper studies the sum-of-ratios version of the classical minimum spanning tree problem. We describe a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The suggested approach specifically addresses the difficulties arising in the case when the number of ratios exceeds two. The efficacy of our approach is demonstrated on randomly generated complete and sparse graph instances. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Oleksii Ursulenko & Sergiy Butenko & Oleg Prokopyev, 2013. "A global optimization algorithm for solving the minimum multiple ratio spanning tree problem," Journal of Global Optimization, Springer, vol. 56(3), pages 1029-1043, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:1029-1043
    DOI: 10.1007/s10898-011-9832-9
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    References listed on IDEAS

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    1. Siegfried Schaible, 1976. "Duality in Fractional Programming: A Unified Approach," Operations Research, INFORMS, vol. 24(3), pages 452-461, June.
    2. Siegfried Schaible, 1976. "Fractional Programming. I, Duality," Management Science, INFORMS, vol. 22(8), pages 858-867, April.
    3. Nimrod Megiddo, 1979. "Combinatorial Optimization with Rational Objective Functions," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 414-424, November.
    4. Gabriel R. Bitran & Thomas L. Magnanti, 1976. "Duality and Sensitivity Analysis for Fractional Programs," Operations Research, INFORMS, vol. 24(4), pages 675-699, August.
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    Cited by:

    1. Shaoning Han & Andrés Gómez & Oleg A. Prokopyev, 2022. "Fractional 0–1 programming and submodularity," Journal of Global Optimization, Springer, vol. 84(1), pages 77-93, September.
    2. Hongtan Sun & Thomas C. Sharkey, 2017. "Approximation guarantees of algorithms for fractional optimization problems arising in dispatching rules for INDS problems," Journal of Global Optimization, Springer, vol. 68(3), pages 623-640, July.
    3. Li, Yifu & Qi, Xiangtong, 2022. "A geometric branch-and-bound algorithm for the service bundle design problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1044-1056.
    4. Samyukta Sethuraman & Sergiy Butenko, 2015. "The maximum ratio clique problem," Computational Management Science, Springer, vol. 12(1), pages 197-218, January.
    5. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.

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