Computing Lower Bounds for Steiner Trees in Road Network Design

In the automated design of road networks an important sub-task is the solution of an instance of the Steiner tree problem, a well known N P-hard problem. In this paper we present the experimental evaluation of a heuristic for the Steiner tree problem used in the design of low volume forest road networks. To evaluate a heuristic it is necessary to compare to the optimum value or a good lower bound on the optimum. Thus, the focus of this paper is on a new approach to compute such lower bounds for the Steiner tree problem in graphs emanating from the automated road network design problem. We evaluated the heuristic on data from a mountainous region of the Swiss Alps. The algorithms and the model were developed in a collaborative project between the Institute of Theoretical Computer Science and the Chair of Land Use Engineering at ETH Zurich.