Optimization Problems in Graphs with Locational Uncertainty

Many discrete optimization problems amount to selecting a feasible set of edges least weight. We consider in this paper the context spatial graphs where positions vertices are uncertain and belong known uncertainty sets. The objective is minimize sum distances chosen for worst their first prove that these [Formula: see text]-hard even when sets consist either all spanning trees or s – t paths. Given hardness, we propose an exact solution algorithm combining integer programming formulations with cutting plane algorithm, identifying cases separation problem can be solved efficiently. also conservative approximation show its equivalence affine decision rule Euclidean distances. compare our algorithms three deterministic reformulations on instances inspired by scientific literature Steiner tree facility location problem. History: Accepted David Alderson, Area Editor Network Optimization: Algorithms & Applications. Supplemental Material: online appendix available at https://doi.org/10.1287/ijoc.2023.1276 .