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Equivalent Formulations of Nonlinear Integer Problems for Efficient Optimization

Author

Listed:
  • Ossama Kettani

    (Sciences de l'Administration Université Laval, Ste-Foy, Québec, P.Q. G1K 7P4, Canada)

  • Muhittin Oral

    (Sciences de l'Administration Université Laval, Ste-Foy, Québec, P.Q. G1K 7P4, Canada)

Abstract

The linearization technique of Glover, which seems to be the most efficient one appearing in the literature, requires the addition of n new continuous variables (unconstrained in sign) and 4n new linear constraints to equivalently represent a 0-1 "quadratic" integer problem with n variables. This paper shows that it is still possible to improve such a procedure. In fact, the number of new continuous variables can be kept at n (but constrained in sign) while further reducing the number of new linear constraints from 4n to 2n.

Suggested Citation

  • Ossama Kettani & Muhittin Oral, 1990. "Equivalent Formulations of Nonlinear Integer Problems for Efficient Optimization," Management Science, INFORMS, vol. 36(1), pages 115-119, January.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:1:p:115-119
    DOI: 10.1287/mnsc.36.1.115
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    Cited by:

    1. Li, Han-Lin & Fang, Shu-Cherng & Huang, Yao-Huei & Nie, Tiantian, 2016. "An enhanced logarithmic method for signomial programming with discrete variables," European Journal of Operational Research, Elsevier, vol. 255(3), pages 922-934.
    2. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
    3. Chang, Ching-Ter, 2000. "An efficient linearization approach for mixed-integer problems," European Journal of Operational Research, Elsevier, vol. 123(3), pages 652-659, June.
    4. Liberatore, Federico & Scaparra, Maria P. & Daskin, Mark S., 2012. "Hedging against disruptions with ripple effects in location analysis," Omega, Elsevier, vol. 40(1), pages 21-30, January.
    5. 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.
    6. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
    7. F. J. Hwang & Yao-Huei Huang, 2021. "An effective logarithmic formulation for piecewise linearization requiring no inequality constraint," Computational Optimization and Applications, Springer, vol. 79(3), pages 601-631, July.

    More about this item

    Keywords

    nonlinear integer programming;

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