A dual variant of Benson's "outer approximation algorithm" for multiple objective linear programming

Authors:
Matthias Ehrgott;Andreas Löhne;Lizhen Shao
Affiliations:
Department of Engineering Science, The University of Auckland, Auckland, New Zealand 1142;NWF II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), Germany 06099;School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China 100083
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

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.