Exact and heuristic solutions for the Minimum Number of Branch Vertices Spanning Tree Problem

Marı́n, Alfredo

doi:10.1016/j.ejor.2015.04.011

Cited by 14 publications

(9 citation statements)

References 18 publications

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“…Cerrone et al (2014) show in their paper that a spanning tree with a minimum number of leaves is better suited to minimising the number of light-splitting devices required in optical networks than two other MST problems. In Marín (2015), the MST problem is adjusted to minimise the number of branches, i.e. nodes with a degree greater than two.…”

Section: Combinatorial Optimisation Of Networkmentioning

confidence: 99%

Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy

et al. 2019

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Plants increasingly exploit high geothermal energy potentials in German district heating networks. Municipal planners need instruments to design the district heating network for geothermal heat. This paper presents a combinatorial mixed-integer linear optimisation model and a three-stage heuristic to determine the minimum-cost district heating systems in municipalities. The central innovations are the ability to optimise both the structure of the heating network and the location of the heating plant, the consideration of partial heat supply from district heating and the scalability to larger municipalities. A comparison of optimisation and heuristic for three exemplary municipalities demonstrates the efficiency of the latter: the optimisation takes between 500% and 1x10 7 % more time than the heuristic. The resulting deviations in the calculated district heating system total investment from the results of the optimisation are in all cases below 5%, and in 80% of cases below 0.3%. The efficiency of the heuristic is further demonstrated by the comparison with the Nearest-Neighbour-Heuristic, which is less efficient and substantially overestimates the total costs by up to 80%. The heuristic can also be used to design district heating networks in holistic energy system optimisations due to the novel possibility of connecting an arbitrary number of buildings to the network. Future work should focus on a more precise consideration of heat losses, as well as taking additional geological and topographical conditions into account.

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Section: Combinatorial Optimisation Of Networkmentioning

confidence: 99%

Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy

et al. 2019

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“…In that article Rossi et al[13] is not cited and consequently no comparison is done. While the approach in Marín[9] seems to be better for some instances of Carrabs et al[2], it fails in finding optimal solutions for several instances of Silva et al[14] within one hour of computation with parallel execution. Those instances are solved to optimality in this work with the same time limit and with a single thread of execution.…”

mentioning

confidence: 94%

“…Computational experiments showed that their approach outperformed the other integer programming techniques available in the literature. Very recently, Marín [9] proposed a preprocessing technique, valid inequalities and a heuristic algorithm, which combined could solve to optimality several instances used in the literature.…”

Section: Introductionmentioning

confidence: 99%

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An effective decomposition approach and heuristics to generate spanning trees with a small number of branch vertices

2016

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Given a graph G = (V, E), the minimum branch vertices problem consists in finding a spanning tree T = (V, E ) of G minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the problem, from which we propose a decomposition approach. The motivation is to break down the problem into several smaller subproblems which are more tractable computationally, and then recombine the obtained solutions to generate a solution to the original problem. We also propose effective constructive heuristics to the problem which take into consideration the problem's structure in order to obtain good feasible solutions. Computational results show that our decomposition approach is very fast and can drastically reduce the size of the subproblems to be solved. This allows a branch and cut algorithm to perform much better than when used over the full original problem. The results also show that the proposed constructive heuristics are highly efficient and generate very good quality solutions, outperforming other heuristics available in the literature in several situations.

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“…They also provide both lower and upper bound for the MBVST using Lagrangian relaxation. In [Mar15], A.Marin presents a branch-and-cut algorithm based on an enforced Integer Programming formulation for the MBVST problem. In [CCR14], C.Cerrone et al present a unied memetic algorithm for the MBVST, the problem of minimize the degree sum of branch vertices (MDST), and the well known Minimum Leaves Problem.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of the Minimum Branch Vertices Spanning Tree Problem

Merabet

Desai

Molnár

2018

Lecture Notes in Computer Science

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Given a connected graph G, a vertex v of G is said to be a branch vertex if its degree is strictly greater than 2. The Minimum Branch Vertices Spanning Tree problem (MBVST) consists in nding a spanning tree of G with the minimum number of branch vertices. This problem has been well studied in the literature and has applications specially for routing in optical networks. In this paper we propose a generalization of this problem. We introduce the notion of k-branch vertex which is a vertex with degree strictly greater than k + 2. The parameter k can be seen as the limit of the capacity of optical splitters to divide the light signal. In order to respect as far as possible this limit, we propose to search a spanning tree of G with the minimum number of k-branch vertices (k-MBVST problem). We propose a proof of NP-hardness of this new problem whatever the value of k. We also propose an ILP formulation of the k-MBVST by generalising the MBVST one. Experimental tests on random graphs show that the number of k-branch vertices increases with graph size but decreases with k as well as with the density. They also show that when k ≥ 4, the number of k-branch vertices is close to zero whatever the size and the density of the tested graph.

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Exact and heuristic solutions for the Minimum Number of Branch Vertices Spanning Tree Problem

Cited by 14 publications

References 18 publications

Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy

Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy

An effective decomposition approach and heuristics to generate spanning trees with a small number of branch vertices

A Generalization of the Minimum Branch Vertices Spanning Tree Problem

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