Paper Info
Title
Semidefinite programming lower bounds and branch-and-bound algorithms for the quadratic minimum spanning tree problem.
Abstract
In this paper, we investigate Semidefinite Programming (SDP) lower bounds for the Quadratic Minimum Spanning Tree Problem (QMSTP). Two SDP lower bounding approaches are introduced here. Both apply Lagrangian Relaxation to an SDP relaxation for the problem. The first one explicitly dualizes the semidefiniteness constraint, attaching to it a positive semidefinite matrix of Lagrangian multipliers. The second relies on a semi-infinite reformulation for the cone of positive semidefinite matrices and dualizes a dynamically updated finite set of inequalities that approximate the cone. These lower bounding procedures are the core ingredient of two QMSTP Branch-and-bound algorithms. Our computational experiments indicate that the SDP bounds computed here are very strong, being able to close at least 70% of the gaps of the most competitive formulation in the literature. As a result, their accompanying Branch-and-bound algorithms are competitive with the best previously available QMSTP exact algorithm in the literature. In fact, one of these new Branch-and-bound algorithms stands out as the new best exact solution approach for the problem.
Year
DOI
Venue
2020
10.1016/j.ejor.2019.07.038
European Journal of Operational Research
Keywords
Field
DocType
Combinatorial Optimization,Spanning Trees,Lagrangian Relaxation,Semidefinite programming,Semi-infinite programming
Branch and bound,Exact algorithm,Lagrange multiplier,Matrix (mathematics),Quadratic equation,Algorithm,Lagrangian relaxation,Semidefinite programming,Mathematics,Minimum spanning tree
Journal
Volume
Issue
ISSN
280
1
0377-2217
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Dilson Almeida Guimarães100.34
Alexandre Salles da Cunha224222.32
Dilson Lucas Pereira3274.15