S.A. Canuto, M.G.C. Resende, and C.C. Ribeiro
Networks, vol. 38, pp. 50-58, 2001
ABSTRACT
Given an undirected graph with prizes associated with
its nodes and weights associated with its edges, the prize-collecting
Steiner tree problem consists in finding a subtree of this graph which
minimizes the sum of the weights of its edges plus the prizes of the
nodes not spanned. In this paper, we describe a multi-start local search
algorithm for the prize-collecting Steiner tree problem, based on the
generation of initial solutions by a primal-dual algorithm using
perturbed node prizes. Path-relinking is used to improve the solutions
found by local search and variable neighborhood search is used as a
post-optimization procedure. Computational experiments involving
different algorithm variants are reported. Our results show that
the local search with perturbations approach found optimal solutions on
nearly all of the instances tested.
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