Minimum spanning trees with neighborhoods: mathematical programming formulations and solution methods
|Author/s||Blanco Izquierdo, Víctor
Fernández Aréizaga, Elena
Puerto Albandoz, Justo
|Department||Universidad de Sevilla. Departamento de Estadística e Investigación Operativa|
|Abstract||This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some ...
This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so 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.
|Funding agencies||Ministerio de Economía y Competitividad (MINECO). España|
|Citation||Blanco Izquierdo, V., Fernández Areizaga, E. y Puerto Albandoz, J. (2017). Minimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods. European Journal of Operational Research, 262 (3), 863-878.|