An oracle-based framework for robust combinatorial optimization

Abstract We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. focus on the discrete scenario case, but our can be extended to other types uncertainty sets such as polytopes or ellipsoids. Concerning underlying certain problem, algorithm is entirely oracle-based, i.e., only requires (primal) solving problem. It thus particularly useful in case problem well-studied its structure cannot directly exploited tailored robust approach, situations where defined implicitly by given software. The idea solve convex relaxation simplicial decomposition main challenge being non-differentiability objective function polytopal uncertainty. resulting dual bounds are then used within branch-and-bound framework optimality. By computational evaluation, we show that method outperforms straightforward linearization approaches minimum spanning tree Moreover, using Concorde solver oracle, computes much better traveling salesman same amount time.