Discrete OptimizationMinimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods

•Minimum Spanning Trees with second order cone-representable neighborhoods and lengths are studied.•Two Mixed Integer Nonlinear models are presented.•A decomposition approach is proposed which is embedded within an branch-and-cut scheme.•An alternate convex search heuristic is developed, by using a biconvex representation.•The results of our computational experiments are reported.

This paper studies Minimum Spanning Trees under incomplete information assuming that it is only known that vertices belong to some neighborhoods that are second order cone representable and distances are measured with a ℓq-norm. Two Mixed Integer Non Linear mathematical programming formulations are presented, based on alternative representations of subtour elimination constraints. A solution scheme is also proposed, resulting from a reformulation suitable for a Benders-like decomposition, which is embedded within an exact branch-and-cut framework. Furthermore, a mathheuristic is developed, which alternates in solving convex subproblems in different solution spaces, and is able to solve larger instances. The results of extensive computational experiments are reported and analyzed.