A fast Voronoi-diagram algorithm with applications to geographical optimization problems

There are many kinds of facility location problems, or "geographical optimization problems", which are appropriately formulated in terms of the Voronoi diagram. Except few quite special problems, we can get a solution to a problem of that kind only by means of numerical approach which involves a large number of function evaluations, where each evaluation requires constructing the Voronoi diagram for a tentative distribution of facilities and computing integrals with reference to that diagram. In such a case, the practical feasibility of the numerical solution of the problem depends largely upon the efficiency of the algorithm to be used for constructing the Voronoi diagram. In this paper, we shall formulate a class of location problems and show that, if we use the Voronoi-diagram algorithm recently proposed by the authors, we can numerically solve considerably large problems within a practicable time.