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Technical Note—Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program

Author

Listed:
  • Fred Glover

    (University of Colorado, Boulder, Colorado)

  • Eugene Woolsey

    (Colorado School of Mines, Golden, Colorado)

Abstract

Rules are given that permit 0-1 polynomial programming problems to be converted to 0-1 linear programming problems in a manner that replaces cross-product terms by continuous rather than integer variables. Since the difficulty of mixed integer programming problems often depends more strongly on the number of integer variables than on the number of continuous variables, such rules are expected to have advantages in practical applications. In addition, the continuous variables automatically receive integer values, and hence our formulation can also be exploited by methods designed to take advantage of a pure integer structure.

Suggested Citation

  • Fred Glover & Eugene Woolsey, 1974. "Technical Note—Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program," Operations Research, INFORMS, vol. 22(1), pages 180-182, February.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:1:p:180-182
    DOI: 10.1287/opre.22.1.180
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    Cited by:

    1. Buchheim, Christoph & Crama, Yves & Rodríguez-Heck, Elisabeth, 2019. "Berge-acyclic multilinear 0–1 optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 102-107.
    2. Saghaei, Mahsa & Ghaderi, Hadi & Soleimani, Hamed, 2020. "Design and optimization of biomass electricity supply chain with uncertainty in material quality, availability and market demand," Energy, Elsevier, vol. 197(C).
    3. Silva, Allyson & Coelho, Leandro C. & Darvish, Maryam, 2021. "Quadratic assignment problem variants: A survey and an effective parallel memetic iterated tabu search," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1066-1084.
    4. Milind Dawande & Monica Johar & Subodha Kumar & Vijay S. Mookerjee, 2008. "A Comparison of Pair Versus Solo Programming Under Different Objectives: An Analytical Approach," Information Systems Research, INFORMS, vol. 19(1), pages 71-92, March.
    5. M. Hosein Zare & Juan S. Borrero & Bo Zeng & Oleg A. Prokopyev, 2019. "A note on linearized reformulations for a class of bilevel linear integer problems," Annals of Operations Research, Springer, vol. 272(1), pages 99-117, January.
    6. 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.
    7. M. Alinaghian & M. Ghazanfari & N. Norouzi & H. Nouralizadeh, 2017. "A Novel Model for the Time Dependent Competitive Vehicle Routing Problem: Modified Random Topology Particle Swarm Optimization," Networks and Spatial Economics, Springer, vol. 17(4), pages 1185-1211, December.
    8. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.
    9. Karthik Natarajan & Dongjian Shi & Kim-Chuan Toh, 2014. "A Probabilistic Model for Minmax Regret in Combinatorial Optimization," Operations Research, INFORMS, vol. 62(1), pages 160-181, February.
    10. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2017. "Linear Reformulation of Polynomial Discrete Programming for Fast Computation," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 108-122, February.
    11. Wang, Haibo & Alidaee, Bahram, 2019. "The multi-floor cross-dock door assignment problem: Rising challenges for the new trend in logistics industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 30-47.
    12. Michael Jünger & Sven Mallach, 2021. "Exact Facetial Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1419-1430, October.

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