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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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
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Abstract	•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.
AbstractList	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. Peer Reviewed •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.
Author	Blanco, Víctor Fernández, Elena Puerto, Justo
Author_xml	– sequence: 1 givenname: Víctor orcidid: 0000-0002-7762-6461 surname: Blanco fullname: Blanco, Víctor email: vblanco@ugr.es organization: Department of Quantitative Methods for Economics and Business, Universidad de Granada, 18011 Granada, Spain – sequence: 2 givenname: Elena orcidid: 0000-0003-4714-0257 surname: Fernández fullname: Fernández, Elena email: e.fernandez@upc.edu organization: Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain – sequence: 3 givenname: Justo surname: Puerto fullname: Puerto, Justo email: puerto@us.es organization: Department of Statistics and Operations Research, Universidad de Sevilla, 41012 Sevilla, Spain
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Cites_doi	10.1287/mnsc.2016.2461 10.1111/j.1467-9787.1978.tb00530.x 10.1016/j.cor.2013.07.023 10.1287/moor.28.4.693.20521 10.1016/0377-2217(93)90145-D 10.1287/opre.29.6.1219 10.1007/BF01580665 10.1137/S0097539794270881 10.1016/S0024-3795(98)10032-0 10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M 10.1590/S0101-74382005000200004 10.1016/0167-6377(91)90028-N 10.1007/s10589-014-9638-z 10.1007/s00453-008-9174-2 10.1145/321043.321046 10.1007/s00186-007-0161-1 10.1007/BF01386316 10.1016/S0305-0548(00)00106-4 10.1007/BF00934810 10.1080/10556788.2011.648932 10.1016/j.ejor.2016.03.002 10.1287/opre.17.4.583 10.1016/0166-218X(94)90008-6 10.1287/opre.24.4.643
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Snippet	•Minimum Spanning Trees with second order cone-representable neighborhoods and lengths are studied.•Two Mixed Integer Nonlinear models are presented.•A... This paper studies Minimum Spanning Trees under incomplete information assuming that it is only known that vertices belong to some neighborhoods that are...
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SubjectTerms	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
Title	Minimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods
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