Oracle-based algorithms for binary two-stage robust optimization

Computational Optimization and Applications, vol. 77, pp. 539–569

Abstract

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

Authors 2

1. Nicolas Kämmerling

   TU Dortmund University

   Affiliation as printed

   Institute of Transport Logistics, TU Dortmund University, Leonhard-Euler-Straße 2, 44227, Dortmund, Germany

   Institute of Transport Logistics, TU Dortmund University, Dortmund, Germany

2. Jannis Kurtz corresponding Aachen Chair for Mathematics of Information Processing

   RWTH Aachen University

   Affiliation as printed

   Chair for Mathematics of Information Processing, RWTH Aachen University, Pontdriesch 12-14, 52062, Aachen, Germany

   Chair for Mathematics of Information Processing RWTH Aachen University Aachen Germany