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

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).

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Acknowledgments

Pedro Castro acknowledges financial support from FEDER (Programa Operacional Factores de Competitividade—COMPETE) and Fundação para a Ciência e Tecnologia through project FCOMP-01-0124-FEDER-020764, and from the Luso-American Foundation under the 2013 Portugal-U.S. Research Networks Program.

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Correspondence to Pedro M. Castro.

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Castro, P.M., Grossmann, I.E. Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems. J Glob Optim 59, 277–306 (2014). https://doi.org/10.1007/s10898-014-0162-6

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Keywords

  • Global optimization
  • Mixed integer nonlinear programming
  • Mixed integer linear programming
  • Scheduling
  • Hydroelectric system