Browsing by Subject "Minimum Spanning Tree"

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Open Access
Min-degree constrained minimum spanning tree problem: New formulation via Miller-Tucker-Zemlin constraints
(Elsevier, 2010-01) Akgun, I.; Tansel, B.
Given an undirected network with positive edge costs and a positive integer d > 2, the minimum-degree constrained minimum spanning tree problem is the problem of finding a spanning tree with minimum total cost such that each non-leaf node in the tree has a degree of at least d. This problem is new to the literature while the related problem with upper bound constraints on degrees is well studied. Mixed-integer programs proposed for either type of problem is composed, in general, of a tree-defining part and a degree-enforcing part. In our formulation of the minimum-degree constrained minimum spanning tree problem, the tree-defining part is based on the Miller-Tucker-Zemlin constraints while the only earlier paper available in the literature on this problem uses single and multi-commodity flow-based formulations that are well studied for the case of upper degree constraints. We propose a new set of constraints for the degree-enforcing part that lead to significantly better solution times than earlier approaches when used in conjunction with Miller-Tucker-Zemlin constraints. © 2009 Elsevier Ltd. All rights reserved
Open Access
A prize collecting Steiner Tree approach to least cost evaluation of grid and off-grid electrification systems
(2017-07) Bölükbaşı, Gizem
The lack of access to electricity in developing countries necessitates spatial electricity planning for guiding sustainable electri cation projects that evaluate the costs of centralized systems vis-a-vis decentralized approaches. Heuristic approaches have been widely used in such electri cation problems to nd feasible, cost e ective solutions; however, most of the time global optimality of these solutions is not guaranteed. Our thesis through its modeling approach provides a new methodology to nd the least cost solution to this electri cation problem. We model the spatial network planning problem as Prize Collecting Steiner Tree problem which would be base for a decision support tool for rural electri cation. This new method is systematically assessed using both randomly generated data and real data from rural regions across Sub- Saharan Africa. Comparative results for the proposed approach and a widely used heuristic method are presented based on computational experiments. Additionally, a bi-objective approach that permits to take carbon emission level into the account is implemented and experimented with numerical data.