Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/317843 
Year of Publication: 
2023
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 88 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 27-51
Publisher: 
Springer US, New York, NY
Abstract: 
We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of uncertainty sets such as polytopes or ellipsoids. Concerning the underlying certain problem, the algorithm is entirely oracle-based, i.e., our approach only requires a (primal) algorithm for solving the certain problem. It is thus particularly useful in case the certain problem is well-studied but its combinatorial structure cannot be directly exploited in a tailored robust optimization approach, or in situations where the underlying problem is only defined implicitly by a given software. The idea of our algorithm is to solve the convex relaxation of the robust problem by a simplicial decomposition approach, the main challenge being the non-differentiability of the objective function in the case of discrete or polytopal uncertainty. The resulting dual bounds are then used within a tailored branch-and-bound framework for solving the robust problem to optimality. By a computational evaluation, we show that our method outperforms straightforward linearization approaches on the robust minimum spanning tree problem. Moreover, using the Concorde solver for the certain oracle, our approach computes much better dual bounds for the robust traveling salesman problem in the same amount of time.
Subjects: 
Robust optimization
Global optimization
Simplicial decomposition
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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