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Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

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  • Pedro Castro
  • Ignacio Grossmann

Abstract

We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal). Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Pedro Castro & Ignacio Grossmann, 2014. "Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems," Journal of Global Optimization, Springer, vol. 59(2), pages 277-306, July.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:2:p:277-306
    DOI: 10.1007/s10898-014-0162-6
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    References listed on IDEAS

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    1. João Teles & Pedro Castro & Henrique Matos, 2013. "Multi-parametric disaggregation technique for global optimization of polynomial programming problems," Journal of Global Optimization, Springer, vol. 55(2), pages 227-251, February.
    2. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    3. Juan Pablo Vielma & Shabbir Ahmed & George Nemhauser, 2010. "Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions," Operations Research, INFORMS, vol. 58(2), pages 303-315, April.
    4. Garcia-Gonzalez, Javier & Parrilla, Ernesto & Mateo, Alicia, 2007. "Risk-averse profit-based optimal scheduling of a hydro-chain in the day-ahead electricity market," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1354-1369, September.
    5. Scott Kolodziej & Pedro Castro & Ignacio Grossmann, 2013. "Global optimization of bilinear programs with a multiparametric disaggregation technique," Journal of Global Optimization, Springer, vol. 57(4), pages 1039-1063, December.
    6. Harjunkoski, Iiro & Westerlund, Tapio & Porn, Ray & Skrifvars, Hans, 1998. "Different transformations for solving non-convex trim-loss problems by MINLP," European Journal of Operational Research, Elsevier, vol. 105(3), pages 594-603, March.
    7. Catalão, J.P.S. & Pousinho, H.M.I. & Mendes, V.M.F., 2011. "Hydro energy systems management in Portugal: Profit-based evaluation of a mixed-integer nonlinear approach," Energy, Elsevier, vol. 36(1), pages 500-507.
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    Cited by:

    1. Marcia Fampa & Jon Lee, 2021. "Convexification of bilinear forms through non-symmetric lifting," Journal of Global Optimization, Springer, vol. 80(2), pages 287-305, June.
    2. Chen, Yang & Odukomaiya, Adewale & Kassaee, Saiid & O’Connor, Patrick & Momen, Ayyoub M. & Liu, Xiaobing & Smith, Brennan T., 2019. "Preliminary analysis of market potential for a hydropneumatic ground-level integrated diverse energy storage system," Applied Energy, Elsevier, vol. 242(C), pages 1237-1247.
    3. Pedro A. Castillo Castillo & Pedro M. Castro & Vladimir Mahalec, 2018. "Global optimization of MIQCPs with dynamic piecewise relaxations," Journal of Global Optimization, Springer, vol. 71(4), pages 691-716, August.
    4. Yu, Guodong & Haskell, William B. & Liu, Yang, 2017. "Resilient facility location against the risk of disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 82-105.

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