A GRASP Heuristic for the Capacitated Minimum Spanning Tree Problem Using a Memory-Based Local Search Strategy
We describe a new neighborhood structure for the capacitated minimum spanning tree problem. This neighborhood structure is used by a local search strategy, leading to good trade-offs between solution quality and computation time. We also propose a GRASP with path-relinking heuristic. It uses a randomized version of a savings heuristic in the construction phase and an extension of the above local search strategy, incorporating some short term memory elements of tabu search. Computational results on benchmark problems illustrate the effectiveness of this approach, which is competitive with the best heuristics in the literature in terms of solution quality. The GRASP heuristic using a memory-based local search strategy improved the best known solution for some of the largest benchmark problem.
KeywordsCapacitated minimum spanning tree Metaheuristics GRASP Local search Neighborhood reduction Short term memory Path-relinking.
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- R.M. Aiex, M.G.C. Resende, P.M. Pardalos, and G. Toraldo. GRASP with pathrelinking for the three-index assignment problem. Technical report, ATamp;T Labs-Research, Florham Park, NJ, 2000. To appear in INFORMS J. on Computing.Google Scholar
- A. Amberg, W. Domschke, and S. Voss. Capacitated minimum spanning trees: Algorithms using intelligent search. Combinatorial Optimization: Theory and Practice, 1: 9–40, 1996.Google Scholar
- P. Festa and M.G.C. Resende. GRASP: An annotated bibliography. In C.C. Ribeiro and P. Hansen, editors, Essays and Surveys in Metaheuristics, pages 325–367. Kluwer, 2002.Google Scholar
- E Glover. Tabu search and adaptive memory programing — Advances, applications and challenges. In R.S. Barr, R.V. Helgason, and J.L. Kennington, editors, Interfaces in Computer Science and Operations Research, pages 1–75. Kluwer, 1996.Google Scholar
- F. Glover. Multi-start and strategic oscillation methods — Principles to exploit adaptive memory. In M. Laguna and J.L. Gonzales-Velarde, editors, Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, pages 1–24. Kluwer, 2000.Google Scholar
- F. Glover and M. Laguna. Tabu Search. Kluwer, 1997.Google Scholar
- J.B. Kruskal. On the shortest spanning tree of a graph and the traveling salesman problem. In Proceedings of the American Mathematical Society, volume 7, pages 48–50, 1956.Google Scholar
- P. Martins. Problema da ârvore de suporte de custo minimo com restriçâo de capacidade: Formulaçöes corn Indice de navel. PhD thesis, Departamento de Estatistica e Investigaçäo Operacional, Universidade de Lisboa, 1999.Google Scholar
- P. Martins, 2001. Personal communication.Google Scholar
- M.G.C. Resende and C.C. Ribeiro. Greedy Randomized Adaptive Search Procedures. In E Glover and G. Kochenberger, editors, Handbook of Metaheuristics, pages 219–249. Kluwer, 2003.Google Scholar
- P.M. Thompson and J.B. Orlin. The theory of cyclic transfer. Technical Report OR200–89, MIT, Operations Research Center, 1989.Google Scholar