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Decomposition for adjustable robust linear optimization subject to uncertainty polytope

Josette Ayoub(josetteayoub***at***hotmail.com)
Michael Poss(michael.poss***at***lirmm.fr)

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 gen- eration 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.

Keywords: Adjustable robust optimization; Uncertainty polytope; Benders decomposition; Mixed-integer linear programming; Network design

Category 1: Robust Optimization

Citation: Minor revision pending for Computational Management Science

Download: [PDF]

Entry Submitted: 11/20/2015
Entry Accepted: 11/20/2015
Entry Last Modified: 11/20/2015

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