Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems |
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Authors: | Pedro M. Castro Ignacio E. Grossmann |
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Affiliation: | 1. Laboratório Nacional de Energia e Geologia, 1649-038?, Lisbon, Portugal 2. Centro de Investiga??o Operacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016, ?Lisbon, Portugal 3. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA?, 15213-3890, USA
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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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