Degree-Constrained k-Minimum Spanning Tree Problem
Joint Authors
Adasme, Pablo
Dehghan Firoozabadi, Ali
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-09
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
Let GV,E be a simple undirected complete graph with vertex and edge sets V and E, respectively.
In this paper, we consider the degree-constrained k-minimum spanning tree (DCkMST) problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d≤k−2.
In particular, in this paper, we consider degree values of d∈2,3.
Notice that DCkMST generalizes both the classical degree-constrained and k-minimum spanning tree problems simultaneously.
In particular, when d=2, it reduces to a k-Hamiltonian path problem.
Application domains where DCkMST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few.
It is easy to see from the literature that the DCkMST problem has not been studied in depth so far.
Thus, our main contributions in this paper can be highlighted as follows.
We propose three mixed-integer linear programming (MILP) models for the DCkMST problem and derive for each one an equivalent counterpart by using the handshaking lemma.
Then, we further propose ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms.
Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy.
We also propose a pure Q-learning algorithm that is competitive with the ACO ones.
Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes.
Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively.
Moreover, we report better solutions than CPLEX for the large-size instances.
Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements.
American Psychological Association (APA)
Adasme, Pablo& Dehghan Firoozabadi, Ali. 2020. Degree-Constrained k-Minimum Spanning Tree Problem. Complexity،Vol. 2020, no. 2020, pp.1-25.
https://search.emarefa.net/detail/BIM-1143850
Modern Language Association (MLA)
Adasme, Pablo& Dehghan Firoozabadi, Ali. Degree-Constrained k-Minimum Spanning Tree Problem. Complexity No. 2020 (2020), pp.1-25.
https://search.emarefa.net/detail/BIM-1143850
American Medical Association (AMA)
Adasme, Pablo& Dehghan Firoozabadi, Ali. Degree-Constrained k-Minimum Spanning Tree Problem. Complexity. 2020. Vol. 2020, no. 2020, pp.1-25.
https://search.emarefa.net/detail/BIM-1143850
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1143850