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

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...

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Bibliographic Details
Published in:Journal of global optimization Vol. 57; no. 1; pp. 51 - 73
Main Authors: Wittmann-Hohlbein, Martina, Pistikopoulos, Efstratios N.
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2013
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Construction
Integer programming
Linear programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Optimization algorithms
Optimization techniques
Process engineering
Real Functions
Studies
Uncertainty
Vectors (mathematics)
United Kingdom > UK
90C31
Multi-parametric programming
Global optimization
90C26
Mixed integer linear programming
90C11
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9895-2