Tabu search for the Steiner problem in graphs

Given an undirected graph with weights associated with its nodes, the Steiner tree problem consists in nding a minimum weight subgraph spanning a given subset of nodes (terminals) of the original graph. In this paper, we describe an improved tabu search algorithm for the Steiner problem in graphs, based on a neighborhood deened by insertions and eliminations of Steiner nodes. Move estimations, elimination tests, and neighborhood reduction techniques are used to speedup the local search, leading to a very fast algorithm with very good results in terms of solution quality. Computational experiments on benchmark problems are reported, comparing the behavior of the improved tabu search with that of other heuristics from the literature. The improved tabu search algorithm clearly outperforms other heuristics in terms of computation times, obtaining better or comparably good solutions.