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Solving two-stage stochastic Steiner tree problems by two-stage branch-and-cut. (English) Zbl 1311.90085

Cheong, Otfried (ed.) et al., Algorithms and computation. 21st international symposium, ISAAC 2010, Jeju Island, Korea, December 15–17, 2010. Proceedings, Part I. Berlin: Springer (ISBN 978-3-642-17516-9/pbk). Lecture Notes in Computer Science 6506, 427-439 (2010).
Summary: We consider the Steiner tree problem under a 2-stage stochastic model with recourse and finitely many scenarios (SSTP). Thereby, edges are purchased in the first stage when only probabilistic information on the set of terminals and the future edge costs is known. In the second stage, one of the given scenarios is realized and additional edges are purchased to interconnect the set of (now known) terminals. The goal is to choose an edge set to be purchased in the first stage while minimizing the overall expected cost of the solution.
We provide a new semi-directed cut-set based integer programming formulation that is stronger than the previously known undirected model. To solve the formulation to provable optimality, we suggest a two-stage branch-and-cut framework, facilitating (integer) L-shaped cuts. The framework itself is also applicable to a range of other stochastic problems.
As SSTP has yet been investigated only from the theoretical point of view, we also present the first computational study for SSTP, showcasing the applicability of our approach and its benefits over solving the extensive form of the deterministic equivalent directly.
For the entire collection see [Zbl 1202.68002].

MSC:

90C15 Stochastic programming
90C10 Integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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