A Combinatorial Branch and Bound for the Min-Max Regret Spanning Tree Problem

Godinho, Noé; Paquete, Luís

doi:10.1007/978-3-030-34029-2_5

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2021

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“…Many robust counterparts of classical optimization problems have been studied in the literature, such as the Robust Shortest Path Problem [Karas ¸an et al, 2001;Catanzaro et al, 2011;Pérez-Galarce et al, 2018] and the Robust Minimum Spanning Tree Problem [Montemanni, 2006;Godinho e Paquete, 2019], and the Robust Shortest Path Tree…”

Section: Related Workmentioning

confidence: 99%

A min-max regret approach for the Steiner Tree Problem with Interval Costs

Carvalho,

Coco,

Noronha

et al. 2021

Preprint

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Let G = (V, E) be a connected graph, where V and E represent, respectively, the node-set and the edge-set. Besides, let Q ⊆ V be a set of terminal nodes, and r ∈ Q be the root node of the graph. Given a weight c ij ∈ N associated to each edge (i, j) ∈ E, the Steiner Tree Problem in graphs (STP) consists in finding a minimum-weight subgraph of G that spans all nodes in Q. In this paper, we consider the Min-max Regret Steiner Tree Problem with Interval Costs (MMR-STP), a robust variant of STP. In this variant, the weight of the edges are not known in advance, but are assumed to vary in the interval [l ij , u ij ]. We develop an ILP formulation, an exact algorithm, and three heuristics for this

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