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Heuristic Search for the Generalized Minimum Spanning Tree Problem

2005
*
INFORMS journal on computing
*

T he

doi:10.1287/ijoc.1040.0077
fatcat:g3qzdwlkrjcz3awyroztityalu
*generalized**minimum**spanning**tree*(GMST)*problem*occurs in telecommunications network planning, where a network of node clusters needs to be connected via a*tree*architecture using exactly one node ... In this paper, we present two*heuristic**search*approaches*for**the*GMST*problem*: local*search*and a genetic algorithm. ... Acknowledgments*The*authors thank Dr. Feremans*for*providing*the*TSPLIB data set. They are also grateful to an anonymous referee*for*suggestions concerning Sollin's adaptation. ...##
###
Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem

2007
*
Journal of Heuristics
*

We consider

doi:10.1007/s10732-007-9047-x
fatcat:dg5l4fh4pzh6zhwjpggk5cz3hi
*the**generalized*version of*the*classical*Minimum**Spanning**Tree**problem*where*the*nodes of a graph are partitioned into clusters and exactly one node from each cluster must be connected. ...*The*third neighborhood type uses Integer Linear Programming to solve parts of*the**problem*to provable optimality. ... Introduction*The**Generalized**Minimum**Spanning**Tree*(GMST)*problem*is an extension of*the*classical*Minimum**Spanning**Tree*(MST)*problem*and is defined as follows. ...##
###
Evolutionary multiobjective combinatorial optimization (EMCO)

2008
*
Proceedings of the 2008 GECCO conference companion on Genetic and evolutionary computation - GECCO '08
*

Diameter-Cost

doi:10.1145/1388969.1389079
dblp:conf/gecco/Kumar08
fatcat:acsog2ea35eijaww2ai7ozm4qi
*Minimum**Spanning**Tree**Problem*69*Problem*Definition Construct a*minimum**spanning**tree*(MST)*for*a given complete graph when a vector of costs is associated with each edge. ... Multiple Edge Cost*Minimum**Spanning**Tree**Problem**Heuristics*and MOEA both results are comparable. ...##
###
An effective genetic algorithm for the minimum-label spanning tree problem

2006
*
Proceedings of the 8th annual conference on Genetic and evolutionary computation - GECCO '06
*

In tests on 27 randomly-

doi:10.1145/1143997.1144097
dblp:conf/gecco/NummelaJ06
fatcat:jqgmdxrsyjagdhmkwfhp26s67i
*generated*instances of*the**minimum*-label*spanning**tree**problem*, versions of*the*GA that apply*generic*operators, with and without*the*local*search*step, perform less well than*the*... Given a connected, undirected graph G with labeled edges,*the**minimum*-label*spanning**tree**problem*seeks a*spanning**tree*on G to whose edges are attached*the*smallest possible number of labels. ... Section 2 below describes*the**minimum*-label*spanning**tree**problem*in more detail, and Section 3 describes*the*greedy*heuristic*. ...##
###
Greedy heuristics and evolutionary algorithms for the bounded minimum-label spanning tree problem

2008
*
Proceedings of the 10th annual conference on Genetic and evolutionary computation - GECCO '08
*

Two greedy

doi:10.1145/1389095.1389217
dblp:conf/gecco/KhaledJ08
fatcat:fnnvbvxqlfco7ic6ud5galtrg4
*heuristics**for**the*unbounded version of*the**problem*are adapted to*the*bounded version. Two genetic algorithms*for**the**problem*encode labeled*spanning**trees*as permutations of G's edges. ... Given an edge-labeled, connected, undirected graph G and a bound r > 1,*the*bounded*minimum*-label*spanning**tree**problem*seeks a*spanning**tree*on G whose edges carry*the*fewest possible labels and in which ... A minimumlabel*spanning**tree*(MLST) on G is one whose edges carry*the*smallest possible number of labels;*the**minimum*-label*spanning**tree**problem*seeks a MLST on G. ...##
###
SOLVING THE DEGREE CONSTRAINED MINIMUM SPANNING TREE PROBLEM USING TABU AND MODIFIED PENALTY SEARCH METHODS

2004
*
Jurnal Teknik Industri
*

In this paper we consider

doaj:c8a5887ace154b67b93ccd56d22ada23
fatcat:5ucgsjsm6zhuno3uzu6zy7rgli
*the*Degree Constrained*Minimum**Spanning**Tree**Problem*. ... This*problem*is concerned with finding, in a given edge weighted graph G (all weights are non-negative),*the**minimum*weight*spanning**tree*T satisfying specified degree restrictions on*the*vertices. ... INTRODUCTION*The*Degree Constrained*Minimum**Spanning**Tree*(DCMST)*problem*is concerned with finding a*minimum*-weight*spanning**tree*whilst satisfying degree requirements on*the*vertices. ...##
###
The Edge-Set Encoding Revisited: On the Bias of a Direct Representation for Trees
[chapter]

2004
*
Lecture Notes in Computer Science
*

In contrast,

doi:10.1007/978-3-540-24855-2_23
fatcat:dyi6aporsna5bp6linqjs2uvay
*the*crossover operator with*heuristics*is biased towards*the*simple*minimum**spanning**tree*(MST) and*generates*more likely*trees*that are MST-like. ... Furthermore,*the*performance of*the*crossover operators is compared*for*OCST*problems*. ... Relevant constraint*minimum**spanning**tree*(MST)*problems*are,*for*example,*the*optimal communication*spanning**tree*(OCST)*problem*, or*the*degree-constrained*minimum**spanning**tree**problem*[1, 2, 3] . ...##
###
A weighted coding in a genetic algorithm for the degree-constrained minimum spanning tree problem

2000
*
Proceedings of the 2000 ACM symposium on Applied computing - SAC '00
*

This paper describes a novel coding of

doi:10.1145/335603.335888
dblp:conf/sac/RaidlJ00
fatcat:32dxoska6zf6ndsipkem2m6pmm
*spanning**trees*in a genetic algorithm*for**the*degree-constrained*minimum**spanning**tree**problem*. ...*For*a connected, weighted graph, this*problem*seeks to identify*the*shortest*spanning**tree*whose degree does not exceed an upper bound k ≥ 2. ... This paper presents a novel coding*for**spanning**trees*in a GA that*searches**for*a degree-constrained*minimum**spanning**tree*. ...##
###
Greedy heuristics for the bounded diameter minimum spanning tree problem

2009
*
ACM Journal of Experimental Algorithmics
*

Given a weighted, connected, undirected graph G and a bound D ≥ 2,

doi:10.1145/1498698.1498699
fatcat:xfhhbxjqsnekzcy4o5vhelhukq
*the*bounded-diameter*minimum**spanning**tree**problem*seeks a*spanning**tree*on G of*minimum*weight whose diameter does not exceed D. ... An evolutionary algorithm*for*this NP-hard*problem*encodes candidate*trees*as permutations of their vertices. ... Figure 1 :*The*center-based*heuristic**for**the*boundeddiameter*minimum**spanning**tree**problem*. ...##
###
On quality performance of heuristic and evolutionary algorithms for biobjective minimum spanning trees

2007
*
Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07
*

We assess

doi:10.1145/1276958.1277394
dblp:conf/gecco/KumarS07
fatcat:qaljqsc73vgxhe56avrjjoo2sq
*the*quality of obtained MOEA solutions in comparison to well-known diameter-constrained*minimum**spanning**tree*(dc-MST) algorithms and further improve MOEA solutions using*problem*-specific knowledge ... In this paper, we consider a biobjective*minimum**spanning**tree**problem*(MOST) and minimize two objectives -*tree*cost and diameter -in terms of Pareto-optimality. ... WORK SUMMARY As*the*dc-MST*problem*is NP-hard*for*all values of k; 4 ≤ k ≤ (n−2), where k and n are diameter and number of nodes in*the**tree*respectively, many*heuristics*/metaheuristics have been proposed ...##
###
A Spanning Tree-based Genetic Algorithm for Distribution Network Reconfiguration
[article]

2020
*
arXiv
*
pre-print

*The*proposed method

*searches*

*spanning*

*trees*of potential configurations and finds

*the*optimal

*spanning*

*tree*using a genetic algorithm in two steps. ... by initial population of GA are filtered out with

*the*help of

*spanning*-

*tree*

*search*algorithm. ...

*The*edge weights are

*problem*specific. While determining

*the*

*minimum*

*spanning*

*tree*,

*the*total sum of all edge weights of a

*spanning*

*tree*is minimized. ...

##
###
The Multilevel Capacitated Minimum Spanning Tree Problem

2006
*
INFORMS journal on computing
*

In this paper, we consider

doi:10.1287/ijoc.1040.0123
fatcat:fi2fhoucenbxfdj4zrd6i7un5a
*the*Multi-Level Capacitated*Minimum**Spanning**Tree*(MLCMST)*problem*, a*generalization*of*the*well-known Capacitated*Minimum**Spanning**Tree*(CMST)*problem*, that allows*for*multiple ... We also develop several*heuristic*procedures*for**the*MLCMST*problem*. First, we present a savings-based*heuristic*. ... One of*the**problems*that deals with*the*design of communication networks is*the*Terminal Layout*Problem*which is typically referred to as*the*Capacitated*Minimum**Spanning**Tree*(CMST)*problem*. ...##
###
Randomized local search, evolutionary algorithms, and the minimum spanning tree problem

2007
*
Theoretical Computer Science
*

*The*analysis of these randomized

*search*

*heuristics*has been started

*for*some well-known

*problems*, and this approach is followed here

*for*

*the*

*minimum*

*spanning*

*tree*

*problem*. ... After motivating this line of research, it is shown that randomized

*search*

*heuristics*find

*minimum*

*spanning*

*trees*in expected polynomial time without employing

*the*global technique of greedy algorithms ... Acknowledgements

*The*second author's work was supported by

*the*Deutsche Forschungsgemeinschaft (DFG) as part of

*the*Collaborative Research Center "Computational Intelligence" (SFB 531) and by

*the*German-Israeli ...

##
###
Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem
[chapter]

2004
*
Lecture Notes in Computer Science
*

*The*analysis of these randomized

*search*

*heuristics*has been started

*for*some well-known

*problems*, and this approach is followed here

*for*

*the*

*minimum*

*spanning*

*tree*

*problem*. ... After motivating this line of research, it is shown that randomized

*search*

*heuristics*find

*minimum*

*spanning*

*trees*in expected polynomial time without employing

*the*global technique of greedy algorithms ... Acknowledgements

*The*second author's work was supported by

*the*Deutsche Forschungsgemeinschaft (DFG) as part of

*the*Collaborative Research Center "Computational Intelligence" (SFB 531) and by

*the*German-Israeli ...

##
###
On Optimal Solutions for the Optimal Communication Spanning Tree Problem

2009
*
Operations Research
*

*The*Optimal Communication

*Spanning*

*Tree*

*Problem*

*Problem*Description

*The*OCST

*problem*[19] seeks a

*tree*that connects all given nodes and satisfies their communication requirements

*for*a

*minimum*total cost ...

*The*OCST

*problem*seeks a

*spanning*

*tree*that connects all

*the*nodes and satisfies their communication requirements at a

*minimum*total cost. ... Acknowledgments

*The*author thanks

*the*referees and

*the*associate editor

*for*valuable comments on

*the*paper. A major part of this work was done while

*the*author was with

*the*University of Mannheim. ...

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