A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming

Outcome space methods construct the set of nondominated points in the objective (outcome) space of a multiple objective linear programme. In this paper, we employ results from geometric duality theory for multiple objective linear programmes to derive a dual variant of Benson’s “outer approximation...

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Bibliographic Details
Published in:Journal of global optimization Vol. 52; no. 4; pp. 757 - 778
Main Authors: Ehrgott, Matthias, Löhne, Andreas, Shao, Lizhen
Format: Journal Article
Language:English
Published: Boston Springer US 01.04.2012
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computer Science
Decision making
Integer programming
Linear programming
Mathematics
Mathematics and Statistics
Objectives
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Linear programming
Duality
Outer approximation
Multiobjective optimization
Vector optimization
Objective space
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:Outcome space methods construct the set of nondominated points in the objective (outcome) space of a multiple objective linear programme. In this paper, we employ results from geometric duality theory for multiple objective linear programmes to derive a dual variant of Benson’s “outer approximation algorithm” to solve multiobjective linear programmes in objective space. We also suggest some improvements of the original version of the algorithm and prove that solving the dual provides a weight set decomposition. We compare both algorithms on small illustrative and on practically relevant examples.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9709-y