Robust solutions to multi-objective linear programs with uncertain data

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Title: Robust solutions to multi-objective linear programs with uncertain data
Authors: Goberna, Miguel A. | Jeyakumar, Vaithilingam | Li, Guoyin | Vicente-Pérez, José
Research Group/s: Laboratorio de Optimización (LOPT)
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa
Keywords: Robust optimization | Multi-objective linear programming | Data uncertainty | Robust feasibility | Robust weakly efficient solutions
Knowledge Area: Estadística e Investigación Operativa
Issue Date: 1-May-2015
Publisher: Elsevier
Citation: European Journal of Operational Research. 2015, 242(3): 730-743. doi:10.1016/j.ejor.2014.10.027
Abstract: In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.
Sponsor: This research was partially supported by the Australian Research Council, Discovery Project DP120100467, the MICINN of Spain, grant number MTM2011-29064-C03-02, and Generalitat Valenciana, grant number ACOMP/2013/062.
ISSN: 0377-2217 (Print) | 1872-6860 (Online)
DOI: 10.1016/j.ejor.2014.10.027
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2014 Elsevier B.V.
Peer Review: si
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INV - DMCTE - Artículos de Revistas

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