A Computational Geometry-based Local Search Algorithm for Planar Location Problem

Constraint-based local search is an important paradigm in the field of constraint programming, particularly when considering very large optimisation problems. In this paper 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. In an optimisation setting it is important that a local search algorithm has access to an incremental way of evaluating the value of its local moves. 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.