An evolution algorithm for the rectilinear Steiner tree problem

Abstract

The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. An evolution algorithm for RSTP based upon the Prim algorithm was presented. The computational results show that the evolution algorithm is better than the previously proposed other heuristics. The average reduction rate of solutions from the evolution algorithm was about 11%, which is almost similar to that of optimal solutions. © Springer-Verlag Berlin Heidelberg 2005.