An oracle-based framework for robust combinatorial optimization

Enrico Bettiol (), Christoph Buchheim (), Marianna De Santis () and Francesco Rinaldi ()
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Enrico Bettiol: TU Dortmund
Christoph Buchheim: TU Dortmund
Marianna De Santis: Sapienza University of Rome
Francesco Rinaldi: University of Padova

Journal of Global Optimization, 2024, vol. 88, issue 1, No 2, 27-51

Abstract: 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.

Keywords: Robust optimization; Global optimization; Simplicial decomposition (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01271-2

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