Minimum spanning trees with neighborhoods: mathematical programming formulations and solution methods

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 meas...

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Detalles Bibliográficos
Autores: Blanco Izquierdo, Víctor, Fernández Aréizaga, Elena, Puerto Albandoz, Justo
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/61450
Acceso en línea:http://hdl.handle.net/11441/61450
https://doi.org/10.1016/j.ejor.2017.04.023
Access Level:acceso abierto
Palabra clave:Minimum spanning trees
Neighborhoods
Mixed integer non linear programming
Second order cone programming
Descripción
Sumario: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.