Title: A note on robustness of the min-max solution to multi-objective linear programs

Authors: Erin K. Doolittle; Garrett M. Dranichak; Karyn Muir; Margaret M. Wiecek

Addresses: Department of Mathematical Sciences, Martin Hall, Clemson University, Clemson, SC 29634, USA ' Department of Mathematical Sciences, Martin Hall, Clemson University, Clemson, SC 29634, USA ' Department of Mathematical Sciences, Martin Hall, Clemson University, Clemson, SC 29634, USA ' Department of Mathematical Sciences, Martin Hall, Clemson University, Clemson, SC 29634, USA

Abstract: The challenge of using scalarising methods in multi-objective optimisation results from the choice of the method, which may not be apparent, and given that a method has been selected, from the choice of the values of the scalarising parameters. In general, these values may be unknown and the decision maker faces a difficult situation of making a choice possibly under a great deal of uncertainty. Due to its effectiveness, the robust optimisation approach of Ben-Tal and Nemirovski is applied to resolve the uncertainty carried in scalarised multi-objective linear programs (MOLPs). A robust counterpart is examined for six different scalarisations of the MOLP yielding robust (weakly) efficient solutions to the original MOLP. The study reveals that the min-max optimal solution emerges as a robust (weakly) efficient solution for five out of the six scalarisations. The implications of this result are also discussed.

Keywords: robust optimisation; multi-objective linear programming; efficient solutions; robust counterpart; scalarisation; uncertainty; min-max solution; multi-objective optimisation.

DOI: 10.1504/IJMCDM.2016.081390

International Journal of Multicriteria Decision Making, 2016 Vol.6 No.4, pp.343 - 365

Received: 18 Jan 2016
Accepted: 14 Sep 2016

Published online: 06 Jan 2017 *

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