A robust optimization based approach to the general solution of mp-MILP problems
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In this work, we focus on the approximate solution of multi-parametric mixed integer linear programming (mp-MILP) problems involving objective function (OFC), left-hand side (LHS) and right-hand side (RHS) uncertainty. A two-step algorithmic procedure is proposed. In the first step a partial immunization against the uncertainty is performed leading to a robust RIM-mp-MILP problem, whereas in the second step explicit optimal solutions of the robust model are derived by applying a decomposition algorithm. Computational studies are presented, demonstrating that (i) the robust RIM-mp-MILP counterpart is less conservative than the conventional robust MILP model, and (ii) the combined robust/multi-parametric procedure is computationally efficient, providing a tight upper bound to the overall global solution of the general mp-MILP problem. 2011 Elsevier B.V.