A randomized Delaunay triangulation heuristic for the Euclidean Steiner tree problem in ℜd

Abstract

We present a heuristic for the Euclidean Steiner tree problem inℜd for d ≥ 2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points.We govern this neighbor generation procedure with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark test problems inℜd for 2 ≤ d ≤ 5. © Springer Science+Business Media, LLC 2010.