On the global solution of multi-parametric mixed integer linear programming problems

Authors:
Martina Wittmann-Hohlbein;Efstratios N. Pistikopoulos
Affiliations:
Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College, London, UK SW7 2BY;Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College, London, UK SW7 2BY
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

This paper deals with the global solution of the general multi-parametric mixed integer linear programming problem with uncertainty in the entries of the constraint matrix, the right-hand side vector, and in the coefficients of the objective function. To derive the piecewise affine globally optimal solution, the steps of a multi-parametric branch-and-bound procedure are outlined, where McCormick-type relaxations of bilinear terms are employed to construct suitable multi-parametric under- and overestimating problems. The alternative of embedding novel piecewise affine relaxations of bilinear terms in the proposed algorithmic procedure is also discussed.