Reactive Tabu Search with Path-Relinking for the Steiner Problem in Graphs
Given an undirected graph with weights associated with its edges, the Steiner tree problem consists in finding a minimum weight subgraph spanning a given subset of nodes (terminals) of the original graph. We describe a reactive tabu search with path-relinking algorithm for the Steiner problem in graphs, based on the extension of a previously developed tabu search algorithm using a neighborhood defined by insertions and eliminations of Steiner nodes. Computational experiments on benchmark problems are reported, comparing the reactive tabu search with other metaheuristic implementations. The reactive tabu search algorithm outperforms other algorithms, obtaining better or comparably good solutions. We also describe a robust parallel implementation based on an independent-thread multiple-walk strategy and report improved computational results on a 32-processor cluster running under Linux.
KeywordsTabu Search Average Relative Error Tabu Search Algorithm Local Search Procedure Steiner Tree Problem
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- J.E. Beasley. OR-Library: Distributing Test Problems by Electronic Mail. Journal of the Operational Research Society, 41:1069–1072, 1990.Google Scholar
- S.A. Canuto, M.G.C. Resende, and C.C. Ribeiro. Local Search with Perturbations for the Prize-Collecting Steiner Tree Problem. To appear in: Networks. Google Scholar
- E.-A. Choukmane. Une heuristique pour le problème de l’arbre de Steiner. RAIRO Recherche Opérationnelle, 12:207–212, 1978.Google Scholar
- V.-D. Cung, S.L. Martins, C.C. Ribeiro, and C. Roucairol. Parallel Strategies for the Implementation of Metaheuristics. In: Essays and Surveys in Metaheuristics, C.C. Ribeiro and P. Hansen, editors, Kluwer, 2001 (this volume).Google Scholar
- C.W. Duin. Steiner’s Problem in Graphs: Approximation, Reduction, Variation. Doctorate Dissertation, Institute of Actuarial Science and Economics, University of Amsterdam, 1994.Google Scholar
- F. Glover. Tabu Search and Adaptive Memory Programing — Advances, Applications and Challenges. In: Interfaces in Computer Science and Operations Research, R.S. Barr, R.V. Helgason, and J.L. Kennington, editors, pages 1–75, Kluwer, 1996.Google Scholar
- Message Passing Interface Forum. MPI: A Message Passing Interface Standard, 1995.Google Scholar