Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
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).
KeywordsGlobal optimization Mixed integer nonlinear programming Mixed integer linear programming Scheduling Hydroelectric system
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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