Minimum 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...

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Bibliographic Details
Published in:European journal of operational research Vol. 262; no. 3; pp. 863 - 878
Main Authors: Blanco, Víctor, Fernández, Elena, Puerto, Justo
Format: Journal Article Publication
Language:English
Published: Elsevier B.V 01.11.2017
Elsevier
Subjects:
05 Combinatorics
05C Graph theory
90 Operations research, mathematical programming
90C Mathematical programming
Classificació AMS
Combinatorial Optimization
Grafs, Teoria de
Graph theory
Investigació operativa
Matemàtica discreta
Matemàtiques i estadística
Minimum Spanning Trees
Mixed Integer Non Linear Programming
Neighborhoods
Programació (Matemàtica)
Programming (Mathematics)
Second order cone programming
Teoria de grafs
Àrees temàtiques de la UPC
Combinatorial Optimization
Minimum Spanning Trees
Neighborhoods
Mixed Integer Non Linear Programming
Second order cone programming
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2017.04.023