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

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 cij ∈ 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 [lij, uij]. We develop an ILP formulation, an exact algorithm, and three heuristics for this ar X iv :2 10 1. 03 34 7v 1 [ m at h. O C ] 9 J an 2 02 1 problem. Computational experiments, performed on generalizations of the classical STP instances, evaluate the efficiency and the limits of the proposed methods.

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