Multi-parametric mixed integer linear programming under global uncertainty

•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 decompos...

Full description

Saved in:
Bibliographic Details
Published in:Computers & chemical engineering Vol. 116; pp. 279 - 295
Main Authors: Charitopoulos, Vassilis M., Papageorgiou, Lazaros G., Dua, Vivek
Format: Journal Article
Language:English
Published: Elsevier Ltd 04.08.2018
Subjects:
Cylindrical algebraic decomposition
Grobner bases
Mixed integer linear programming
Multi-parametric programming
Optimisation under uncertainty
Process scheduling
Multi-parametric programming
Cylindrical algebraic decomposition
Mixed integer linear programming
Grobner bases
Process scheduling
Optimisation under uncertainty
ISSN:0098-1354, 1873-4375
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•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]
ISSN:0098-1354
1873-4375
DOI:10.1016/j.compchemeng.2018.04.015