Parallel local search for Steiner trees in graphs

This paper discusses sequential and parallel local search for the Steiner tree problem in graphs. We introduce novel neighborhoods whose computational time and space complexity is smaller than those known in the literature. We present computational results for benchmark instances and instances derived from real-world traveling salesman problem instances, which contain up to 18,512 vertices and 325,093 edges. These results show that good-quality solutions can be obtained in moderate running times. Furthermore, we present a parallel local search algorithm based on multiple-step parallelism and an optimal polynomial-time combination function. Computational results show that good speed-ups can be obtained without loss in quality of final solutions.