Faster Algorithms for Min-max-min Robustness for Combinatorial Problems with Budgeted Uncertainty

André Chassein (1) , Marc Goerigk (1) , Jannis Kurtz , Michael Poss (2)

1 Fachbereich Mathematik [Kaiserslautern]
2 MAORE - Methods, Algorithms for Operations REsearch

We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of k solutions. This approach is appropriate for decision problems under uncertainty where the implementation of decisions requires preparing the ground. We focus on the case that the set of possible scenarios is described through a budgeted uncertainty set and provide three algorithms for the problem. The first algorithm solves heuristically the dualized problem, a non-convex mixed-integer non-linear program (MINLP), via an alternating optimization approach. The second algorithm solves the MINLP exactly for k = 2 through a dedicated spatial branch-and-bound algorithm. The third approach enumerates k-tuples, relying on strong bounds to avoid a complete enumeration. We test our methods on shortest path instances that were used in the previous literature and on randomly generated knapsack instances, and find that our methods considerably outperform previous approaches. Many instances that were previously not solved within hours can now be solved within few minutes, often even faster.

Mots clés: combinatorial optimization; robust optimization; k-adaptability; budgeted uncertainty; branch-and-bound algorithms

Domaines: Recherche opérationnelle [math.OC]

André Chassein, Marc Goerigk, Jannis Kurtz, Michael Poss. Faster Algorithms for Min-max-min Robustness for Combinatorial Problems with Budgeted Uncertainty. European Journal of Operational Research, 2019, ⟨10.1016/j.ejor.2019.05.045⟩. ⟨hal-02171552⟩