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Fenchel Cutting Planes for Integer Programs

Author

Listed:
  • E. Andrew Boyd

    (Texas A&M University, College Station, Texas)

Abstract

A technique for generating cutting planes for integer programs is introduced that is based on the ability to optimize a linear function on a polyhedron rather than explicit knowledge of the underlying polyhedral structure of the integer program. The theoretical properties of the cuts and their relationship to Lagrangian relaxation are discussed, the cut generation procedure is described, and computational results are presented.

Suggested Citation

  • E. Andrew Boyd, 1994. "Fenchel Cutting Planes for Integer Programs," Operations Research, INFORMS, vol. 42(1), pages 53-64, February.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:1:p:53-64
    DOI: 10.1287/opre.42.1.53
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    Citations

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    Cited by:

    1. Raphael Kramer & Manuel Iori & Thibaut Vidal, 2020. "Mathematical Models and Search Algorithms for the Capacitated p -Center Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 444-460, April.
    2. Dorneles, Árton P. & de Araújo, Olinto C.B. & Buriol, Luciana S., 2017. "A column generation approach to high school timetabling modeled as a multicommodity flow problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 685-695.
    3. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    4. Mitchell, John E., 1997. "Fixing variables and generating classical cutting planes when using an interior point branch and cut method to solve integer programming problems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 139-148, February.
    5. Christian Va Karsten & Stefan Ropke & David Pisinger, 2018. "Simultaneous Optimization of Container Ship Sailing Speed and Container Routing with Transit Time Restrictions," Transportation Science, INFORMS, vol. 52(4), pages 769-787, August.
    6. Li, Dongjun & Islam, Dewan Md Zahurul & Robinson, Mark & Song, Dong-Ping & Dong, Jing-Xin & Reimann, Marc, 2024. "Network revenue management game in the railway industry: Stackelberg equilibrium, global optimality, and mechanism design," European Journal of Operational Research, Elsevier, vol. 312(1), pages 240-254.
    7. Kerem Akartunalı & Ioannis Fragkos & Andrew J. Miller & Tao Wu, 2016. "Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 766-780, November.
    8. Yang, Zhen & Chu, Feng & Chen, Haoxun, 2012. "A cut-and-solve based algorithm for the single-source capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 221(3), pages 521-532.
    9. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    10. Liang Chen & Wei-Kun Chen & Mu-Ming Yang & Yu-Hong Dai, 2021. "An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron," Journal of Global Optimization, Springer, vol. 81(3), pages 659-689, November.
    11. Gyana Parija & Radu Gadidov & Wilbert Wilhelm, 1999. "A Facet Generation Procedure for Solving 0/1 Integer Programs," Operations Research, INFORMS, vol. 47(5), pages 789-791, October.
    12. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    13. M T Ramos & J Sáez, 2005. "Solving capacitated facility location problems by Fenchel cutting planes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 297-306, March.
    14. Fritz Bökler & Sophie N. Parragh & Markus Sinnl & Fabien Tricoire, 2024. "An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 263-290, August.
    15. Saravanan Venkatachalam & Lewis Ntaimo, 2023. "Integer set reduction for stochastic mixed-integer programming," Computational Optimization and Applications, Springer, vol. 85(1), pages 181-211, May.

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