Determination of Weights of Generalized Voronoi Regions Using Tabu Search and Applications(Theory and Methodology)

Abstract

Every Voronoi region has a polygonal form and has a point which is called generatrix. In this paper, we treat the generalized Voronoi regions as Voronoi regions with weighted generatrices. If the weights of all generatrices are identical, these regions conform with usual Voronoi regions. Suppose a set of points which are not generatrices and usual generatrices are distributed on a plane. Proposed procedures in this paper can find a set of suitable generatrix weights so as to include points in the respective region in accordance with the specified proportion. Tabu search is used to determine generatrix weights. An application of these generalized Voronoi regions is introduced. If points and generatrices are regarded as cities and depots, respectively, this proposal can be applied to the vehicle routing problem (VRP).