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...
| Autores: | , , |
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| 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 |
| 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. |
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