Models and branch‐and‐cut algorithms for the Steiner tree problem with revenues, budget and hop constraints

@article{Costa2009ModelsAB,
  title={Models and branch‐and‐cut algorithms for the Steiner tree problem with revenues, budget and hop constraints},
  author={Alysson M. Costa and Jean-François Cordeau and Gilbert Laporte},
  journal={Networks},
  year={2009},
  volume={53}
}
The Steiner tree problem with revenues, budget and hop constraints is a variant of the Steiner tree problem with two main modifications: (a) besides the costs associated with arcs, there are also revenues associated with the vertices, and (b) there are additional budget and hop constraints, which impose limits on the total cost of the network and on the number of edges between any vertex and the root, respectively. This article introduces and compares several mathematical models for this… 
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Branch-and-Price for the Steiner Tree Problem with Revenues , Budget and Hop Constraints
This thesis deals with the Steiner tree problem with revenues, budget and hop constraints (STPRBH), an NP-hard combinatorial optimization problem with applications in telecommunications network…
Solving the steiner tree problem with revenues, budget and hop constraints to optimality
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This work investigates the Steiner tree problem with revenues, budget and hop constraints (STPRBH) on graph, and proposes an enhanced formulation based on the classical work of Miller, Tucker, and Zemlin by using additional set of variables representing the rank-order of visiting the nodes.
A node-based layered graph approach for the Steiner tree problem with revenues, budget and hop-constraints
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A novel generic way to model hop-constrained tree problems as integer linear programs and apply it to the Steiner tree problem, based on the concept of layered graphs, which contains much less variables and allows to tackle large-scale instances and/or instances with large hop-limits.
The Multi-period Prize-collecting Steiner Tree Problem with Budget Constraints
The classical Prize-collecting Steiner Tree Problem aims at finding a connected subgraph that maximizes the revenues collected from connected vertices minus the costs to utilize the connecting edges.…
Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints
On the hop-constrained Steiner tree problems
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It is shown that the linear programming relaxation of the partial-ordering based model is stronger than that of the assignment model for the hop-constrained Steiner tree problem; this remains true also for a class of hop- Constrained problems, including theHop-Constrained minimum spanning tree problem, the Steiners tree problem with revenues, budgets and hop constraints.
An efficient algorithm for the Steiner Tree Problem with revenue, bottleneck and hop objective functions
The Steiner Tree Problem with Delays: A compact formulation and reduction procedures
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Two novel variants of the well-known Steiner tree problem in graphs are proposed that are motivated by applications in secure strategic telecommunication network design and incorporate problem specific valid inequalities that are crucial in order to solve these problems.
Iterated Greedy Algorithms for the Hop-Constrained Steiner Tree Problem
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Three iterative greedy algorithms are described to find efficient optimized solution to solve HCST on both sparse and dense graphs, and in the third algorithm, the idea of Kruskal algorithm is adopted for the HCST problem to reach a better solution.
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