Networks
A faster approximation algorithm for the Steiner problem in graphs
Information Processing Letters
Steiner's problem in graphs: heuristic methods
Discrete Applied Mathematics - Special issue: combinatorial methods in VLSI
The Steiner tree polytope and related polyhedra
Mathematical Programming: Series A and B
Tabu Search
A Parallel GRASP for the Steiner Problem in Graphs
IRREGULAR '98 Proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel
Probability Distribution of Solution Time in GRASP: An Experimental Investigation
Journal of Heuristics
A Parallel GRASP Heuristic for the 2-Path Network Design Problem (Research Note)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
New benchmark instances for the Steiner problem in graphs
Metaheuristics
Parallelization of local search for Euclidean Steiner tree problem
Proceedings of the 44th annual Southeast regional conference
HM '08 Proceedings of the 5th International Workshop on Hybrid Metaheuristics
Benchmarking a wide spectrum of metaheuristic techniques for the radio network design problem
IEEE Transactions on Evolutionary Computation
A Survey of Parallel and Distributed Algorithms for the Steiner Tree Problem
International Journal of Parallel Programming
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In this paper, we present a parallel greedy randomized adaptive search procedure (GRASP) for the Steiner problem in graphs. GRASP is a two-phase metaheuristic. In the first phase, solutions are constructed using a greedy randomized procedure. Local search is applied in the second phase, leading to a local minimum with respect to a specified neighborhood. In the Steiner problem in graphs, feasible solutions can be characterized by their non-terminal nodes (Steiner nodes) or by their key-paths. According to this characterization, two GRASP procedures are described using different local search strategies. Both use an identical construction procedure. The first uses a node-based neighborhood for local search, while the second uses a path-based neighborhood. Computational results comparing the two procedures show that while the node-based variant produces better quality solutions, the path-based variant is about twice as fast. A hybrid GRASP procedure combining the two neighborhood search strategies is then proposed. Computational experiments with a parallel implementation of the hybrid procedure are reported, showing that the algorithm found optimal solutions for 45 out of 60 benchmark instances and was never off by more than 4% of the optimal solution value. The average speedup results observed for the test problems show that increasing the number of processors reduces elapsed times with increasing speedups. Moreover, the main contribution of the parallel algorithm concerns the fact that larger speedups of the same order of the number of processors are obtained exactly for the most difficult problems.