Minimum Spanning Trees with neighborhoods: mathematical programming formulations and solution methods

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...

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Detalles Bibliográficos
Autores: Blanco, Víctor, Fernández Aréizaga, Elena|||0000-0003-4714-0257, Puerto Albandoz, Justo
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/114229
Acceso en línea:https://hdl.handle.net/2117/114229
https://dx.doi.org/10.1016/j.ejor.2017.04.023
Access Level:acceso abierto
Palabra clave:Graph theory
Programming (Mathematics)
Combinatorial Optimization
Minimum Spanning Trees
Neighborhoods
Mixed Integer Non Linear Programming
Second order cone programming
Grafs, Teoria de
Programació (Matemàtica)
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
Descripción
Sumario: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.