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

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

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Article ID: iaor20123060
Volume: 52
Issue: 4
Start Page Number: 757
End Page Number: 778
Publication Date: Apr 2012
Journal: Journal of Global Optimization
Authors: , ,
Keywords: programming: multiple criteria
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.

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