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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This work has been partially supported by the National Science Foundation of China (No. 81000650), the PhD Programs Foundation of the Ministry of Education of China (No. 20100006120016) and China Postdoctoral Science Foundation (No. 20100470206).
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Ehrgott, M., Löhne, A. & Shao, L. A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming. J Glob Optim 52, 757–778 (2012). https://doi.org/10.1007/s10898-011-9709-y
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DOI: https://doi.org/10.1007/s10898-011-9709-y