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Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
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Abstract(s)
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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Keywords
Global optimization Mixed-integer nonlinear programming Mixed-integer linear programming Scheduling Hydroelectric system
Pedagogical Context
Citation
Castro, P.M.; Grossmann, I.E. - Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems. In: Journal of Global Optimization, 2014, Vol. 59, nº 2-3, p. 277-306