Local search with perturbations for the prize-collecting Steiner tree problem in graphs

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