Improved solution strategies for dominating trees

Adasme, Pablo; Andrade, Rafael; Leung, Janny; Lisser, Abdel

doi:10.1016/j.eswa.2018.01.031

Cited by 13 publications

(13 citation statements)

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“…First, notice that the constraint (6) imposes the condition that any tree formed with nodes in S contains exactly |S| − 1 arcs. However, the constraints (10) ensure that the number of arcs entering node j ∈ V is at most one if and only if y j � 1. Similarly, the constraints (11) ensure that the number of incoming and outgoing arcs in node j ∈ V can be at most |V| − 1 if and only if y j � 1.…”

Section: Milp Formulationsmentioning

confidence: 99%

“…. , (v j , v 1 ) for some j ∈ S. is particular case is avoided by means of the constraints (6) and (10), which finally ensure that the digraph is connected with |S| − 1 directed arcs while avoiding the fact that a particular node has more than one incoming arc. Consequently, by dropping the directions of each arc, we obtain an undirected tree topology.…”

Section: Milp Formulationsmentioning

confidence: 99%

“…Finally, the constraints (12) limit the domain of the decision variables, thus concluding the proof. □ Notice that P 1 is constructed based on a classical formulation of the p-Median problem and a directed Miller-Tucker-Zemlin characterization of the spanning tree polytope [10,21,22].…”

Section: Milp Formulationsmentioning

confidence: 99%

“…If two facility nodes are located near a certain distance, then at most, one of them can be selected for the tree backbone. Finally, users can connect to the resulting subset S. Notice that forming a tree backbone with facilities is an efficient strategy to ensure connectivity in a network [5,[8][9][10][11][12]. A unit disk graph is the resulting graph obtained by intersecting several unit disks in the Euclidean plane where each vertex corresponds to a center of each disk and with edges connecting them whenever the corresponding vertices lie within a constant (unit) distance of each other.…”

Section: Introductionmentioning

confidence: 99%

“…We propose four compact polynomial formulations based on classical and set covering p-Median models in order to minimize the total connection cost distance between facilities and between customers and facilities simultaneously [10,20,21]. However, the tree to be formed with S is modelled with Miller-Tucker-Zemlin (MTZ) and path orienteering constraints, respectively [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Facility Location with Tree Topology and Radial Distance Constraints

Adasme

Firoozabadi

2019

Complexity

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Let G d (V, E d ) be an input disk graph with a set of facility nodes V and a set of edges E d connecting facilities in V. In this paper, we minimize the total connection cost distances between a set of customers and a subset of facility nodes S ⊆ V and among facilities in S, subject to the condition that nodes in S simultaneously form a spanning tree and an independent set according to graphs G d and G d , respectively, where G d is the complement of G d . Four compact polynomial formulations are proposed based on classical and set covering p-Median formulations. However, the tree to be formed with S is modelled with Miller-Tucker-Zemlin (MTZ) and path orienteering constraints. Example domains where the proposed models can be applied include complex wireless and wired network communications, warehouse facility location, electrical power systems, water supply networks, and transportation networks, to name a few. e proposed models are further strengthened with clique valid inequalities which can be obtained in polynomial time for disk graphs. Finally, we propose Kruskal-based heuristics and metaheuristics based on guided local search and simulated annealing strategies. Our numerical results indicate that only the MTZ constrained models allow obtaining optimal solutions for instances with up to 200 nodes and 1000 users. In particular, tight lower bounds are obtained with all linear relaxations, e.g., less than 6% for most of the instances compared to the optimal solutions. In general, the MTZ constrained models outperform path orienteering ones. However, the proposed heuristics and metaheuristics allow obtaining near-optimal solutions in signi cantly short CPU time and tight feasible solutions for large instances of the problem.

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Section: Milp Formulationsmentioning

confidence: 99%

Section: Milp Formulationsmentioning

confidence: 99%