Multi-parametric mixed integer linear programming under global uncertainty - Charitopoulos, Vassilis M.; Papageorgiou, Lazaros G.; Dua, Vivek (Computers & chemical engineering, 2018)
•An algorithm for the exact solution of multi-parametric mixed integer linear programming problems under global uncertainty is proposed.•The uncertain parameters along with integer variables are treated as symbolic expressions.•Exact non-convex CRs are computed through cylindrical algebraic decompositions.•The algorithm scales favourably with the no. of uncertain parameters considered. Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. Multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the right-hand side (RHS) and in the objective function’s coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm. [Display omitted]