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Heuristic Search for the Generalized Minimum Spanning Tree Problem

Bruce Golden, S. Raghavan, Daliborka Stanojević
2005 INFORMS journal on computing  
T he 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.  ... 
doi:10.1287/ijoc.1040.0077 fatcat:g3qzdwlkrjcz3awyroztityalu

Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem

Bin Hu, Markus Leitner, Günther R. Raidl
2007 Journal of Heuristics  
We consider 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.  ... 
doi:10.1007/s10732-007-9047-x fatcat:dg5l4fh4pzh6zhwjpggk5cz3hi

Evolutionary multiobjective combinatorial optimization (EMCO)

Rajeev Kumar
2008 Proceedings of the 2008 GECCO conference companion on Genetic and evolutionary computation - GECCO '08  
Diameter-Cost 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.  ... 
doi:10.1145/1388969.1389079 dblp:conf/gecco/Kumar08 fatcat:acsog2ea35eijaww2ai7ozm4qi

An effective genetic algorithm for the minimum-label spanning tree problem

Jeremiah Nummela, Bryant A. Julstrom
2006 Proceedings of the 8th annual conference on Genetic and evolutionary computation - GECCO '06  
In tests on 27 randomly-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.  ... 
doi:10.1145/1143997.1144097 dblp:conf/gecco/NummelaJ06 fatcat:jqgmdxrsyjagdhmkwfhp26s67i

Greedy heuristics and evolutionary algorithms for the bounded minimum-label spanning tree problem

Arindam Khaled, Bryant A. Julstrom
2008 Proceedings of the 10th annual conference on Genetic and evolutionary computation - GECCO '08  
Two greedy 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.  ... 
doi:10.1145/1389095.1389217 dblp:conf/gecco/KhaledJ08 fatcat:fnnvbvxqlfco7ic6ud5galtrg4

SOLVING THE DEGREE CONSTRAINED MINIMUM SPANNING TREE PROBLEM USING TABU AND MODIFIED PENALTY SEARCH METHODS

Wamiliana Wamiliana
2004 Jurnal Teknik Industri  
In this paper we consider 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.  ... 
doaj:c8a5887ace154b67b93ccd56d22ada23 fatcat:5ucgsjsm6zhuno3uzu6zy7rgli

The Edge-Set Encoding Revisited: On the Bias of a Direct Representation for Trees [chapter]

Carsten Tzschoppe, Franz Rothlauf, Hans-Josef Pesch
2004 Lecture Notes in Computer Science  
In contrast, 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] .  ... 
doi:10.1007/978-3-540-24855-2_23 fatcat:dyi6aporsna5bp6linqjs2uvay

A weighted coding in a genetic algorithm for the degree-constrained minimum spanning tree problem

Günther R. Raidl, Bryant A. Julstrom
2000 Proceedings of the 2000 ACM symposium on Applied computing - SAC '00  
This paper describes a novel coding of 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.  ... 
doi:10.1145/335603.335888 dblp:conf/sac/RaidlJ00 fatcat:32dxoska6zf6ndsipkem2m6pmm

Greedy heuristics for the bounded diameter minimum spanning tree problem

Bryant A. Julstrom
2009 ACM Journal of Experimental Algorithmics  
Given a weighted, connected, undirected graph G and a bound D ≥ 2, 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.  ... 
doi:10.1145/1498698.1498699 fatcat:xfhhbxjqsnekzcy4o5vhelhukq

On quality performance of heuristic and evolutionary algorithms for biobjective minimum spanning trees

Rajeev Kumar, Pramod Kumar Singh
2007 Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07  
We assess 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  ... 
doi:10.1145/1276958.1277394 dblp:conf/gecco/KumarS07 fatcat:qaljqsc73vgxhe56avrjjoo2sq

A Spanning Tree-based Genetic Algorithm for Distribution Network Reconfiguration [article]

Mukesh Gautam, Narayan Bhusal, Mohammed Benidris, Sushil J. Louis
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.  ... 
arXiv:2008.07908v1 fatcat:yacvxjnxozbedjgcjqpmqjk42m

The Multilevel Capacitated Minimum Spanning Tree Problem

Ioannis Gamvros, Bruce Golden, S. Raghavan
2006 INFORMS journal on computing  
In this paper, we consider 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.  ... 
doi:10.1287/ijoc.1040.0123 fatcat:fi2fhoucenbxfdj4zrd6i7un5a

Randomized local search, evolutionary algorithms, and the minimum spanning tree problem

Frank Neumann, Ingo Wegener
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  ... 
doi:10.1016/j.tcs.2006.11.002 fatcat:ohrhbhkmrfahpghg3g43hwknru

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

Frank Neumann, Ingo Wegener
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  ... 
doi:10.1007/978-3-540-24854-5_73 fatcat:3f6gs4l7m5gwph4so6fqh33uki

On Optimal Solutions for the Optimal Communication Spanning Tree Problem

Franz Rothlauf
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.  ... 
doi:10.1287/opre.1080.0592 fatcat:xmzlromdg5b3zlryo5wiopmvtm
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