A Computational Geometry-Based Local Search Algorithm for Planar Location Problems

Constraint-based local search is an important paradigm in the field of constraint programming, particularly when considering very large optimisation problems. We are motivated by applications in areas such as telecommunications network design, warehouse location and other problems in which we wish to select an optimal set of locations from a two dimensional plane. The problems we are interested in are so large that they are ideal candidates for constraint-based local search methods. Maintaining the objective function incrementally is often a key element for efficient local search algorithms. In the case of two dimensional plane problems, we can often achieve incrementality by exploiting computational geometry. In this paper we present a novel approach to solving a class of placement problems for which Voronoi cell computation can provide an efficient form of incrementality. We present empirical results demonstrating the utility of our approach against the current state of the art.