Knowledge Guided Tabu Search for the Prize Collecting Steiner Tree Problem in Graphs

Given an undirected graph with prizes associated with its vertices and costs associated with its edges, the prize-collecting Steiner tree problem in graphs (PCSPG) consists of finding a subtree of this graph, so as to minimize the sum of the costs of its edges plus the prizes of the vertices not spanned. In this paper, we propose a knowledge guided tabu search (named K-TS) algorithm for the PCSPG which integrates several new (and important) ingredients, including two path-based move operators for generating neighboring solutions, a tabu search procedure for local optimization, two knowledge guided perturbation operators for escaping from local optimum, as well as a knowledge updating mechanism. Specially, for instances with special structures, we implement an innovative swap-vertex move operator which is shown to be significantly effective. Experiments results based on a subset of representative PCSPG benchmarks show that, the proposed K-TS algorithm is overall highly effective, especially on several groups of special instances which are extremely difficult for the existing algorithms. K-TS also produces a number of remarkable results on the rooted version of PCSPG and the classical SPG.