Decomposition for adjustable robust linear optimization subject to uncertainty polytope

Josette Ayoub Michael Poss 1
1 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We present in this paper a general decomposition framework to solve exactly adjustable robust linear optimization problems subject to poly-tope uncertainty. Our approach is based on replacing the polytope by the set of its extreme points and generating the extreme points on the fly within row generation or column-and-row generation algorithms. The novelty of our approach lies in formulating the separation problem as a feasibility problem instead of a max-min problem as done in recent works. Applying the Farkas lemma, we can reformulate the separation problem as a bilinear program, which is then linearized to obtained a mixed-integer linear programming formulation. We compare the two algorithms on a robust telecommunications network design under demand uncertainty and budgeted uncertainty polytope. Our results show that the relative performance of the algorithms depend on whether the budget is integer or fractional.
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Submitted on : Tuesday, April 12, 2016 - 10:54:03 AM
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Josette Ayoub, Michael Poss. Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Computational Management Science, Springer Verlag, 2016, 13 (2), pp.219-239. ⟨10.1007/s10287-016-0249-2⟩. ⟨hal-01301374⟩



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