Local search for the Steiner tree problem in the Euclidean plane
Most heuristics for the Steiner tree problem in the Euclidean plane perform a series of iterative improvements using the minimum spanning tree as an initial solution. We may therefore characterize them as local search heuristics. In this paper, we first give a survey of existing heuristic approaches from a local search perspective, by setting up solution spaces and neighbourhood structures. Secondly, we present a new general local search approach which is based on a list of full Steiner trees constructed in a preprocessing phase. This list defines a solution space on which three neighbourhood structures are proposed and evaluated. Computational results show that this new approach is very competitive from a costbenefit point of view. Furthermore, it has the advantage of being easy to apply to the Steiner tree problem in other metric spaces and to obstacle avoiding variants.
local search steiner trees heuristics survey