A branch and bound method for the solution of multiparametric mixed integer linear programming problems

In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch and bo...

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Bibliographic Details
Published in:Journal of global optimization Vol. 59; no. 2-3; pp. 527 - 543
Main Authors: Oberdieck, Richard, Wittmann-Hohlbein, Martina, Pistikopoulos, Efstratios N.
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2014
Springer
Springer Nature B.V
Subjects:
Algorithms
Branch & bound algorithms
Computer Science
Integer programming
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Mixed integer
Operations Research/Decision Theory
Optimization
Real Functions
Strategy
Studies
Systems engineering
Variables
Vectors (mathematics)
Branch and bound
Multiparametric programming
Mixed integer linear programming
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch and bound strategy that involves the solution of a multiparametric linear programming sub-problem at leaf nodes and appropriate comparison procedures to update the tree. McCormick relaxation procedures are employed to overcome the presence of bilinear terms in the model. The algorithm generates an envelope of parametric profiles, containing the optimal solution of the mp-MILP problem. The parameter space is partitioned into polyhedral convex critical regions. Two examples are presented to illustrate the steps of the proposed algorithm.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0143-9