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… 
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
TLDR
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
TLDR
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
TLDR
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.
Branch-and-Cut Algorithms for Steiner Tree Problems with Privacy Conflicts
TLDR
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
TLDR
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.
...
...

References

SHOWING 1-10 OF 49 REFERENCES
Steiner Tree Problems With Profits
Abstract This is a survey of the Steiner tree problem with profits, a variation of the classical Steiner problem where, besides the costs associated with edges, there are also revenues associated
The node-weighted steiner tree problem
TLDR
This article analyzes a special case of that problem, where the set of nodes, which must be included in the solution tree, consists of a single node, and all node weights are negative.
Solving the Prize-Collecting Steiner Tree Problem to Optimality
TLDR
This work presents an efficient implementation of PCST on a directed graph model and connectivity inequalities corresponding to cuts in the graph that solves all benchmark instances from the literature to optimality, including eight for which the optimum was not known.
Solving Steiner tree problems in graphs to optimality
TLDR
The implementation of a branch-and-cut algorithm for solving Steiner tree problems in graphs based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics is presented.
Using Hop-Indexed Models For Constrained Spanning and Steiner Tree Models
TLDR
Several models for network design problems involve only one set of binary variables, with one and only one variable X ij corresponding to each arc of the underlying graph, which may reduce considerably the number of constraints needed to derive a valid model for the same problem.
The Steiner tree problem with hop constraints
  • S. Voß
  • Mathematics
    Ann. Oper. Res.
  • 1999
TLDR
A simple heuristic is developed and an exchange procedure based on the tabu searchmetastrategy is applied to improve given solutions of the Steiner tree problem with hop constraints.
A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs
Combining a Memetic Algorithm with Integer Programming to Solve the Prize-Collecting Steiner Tree Problem
TLDR
A new algorithmic framework for the prize-collecting Steiner tree problem on a graph with edge costs and vertex profits is developed, consisting of three main parts: edges, vertices and profit.
Local search with perturbations for the prize‐collecting Steiner tree problem in graphs
TLDR
A multistart local search algorithm for the prize‐collecting Steiner tree problem is described, based on the generation of initial solutions by a primal‐dual algorithm using perturbed node prizes, which found optimal solutions on nearly all of the instances tested.
Multicommodity flow models for spanning trees with hop constraints
...
...