Design of Experiments for a multi-objective partitioning problem

In this paper we present a factorial statistical experiment for a combinatorial optimization problem bi-objective, which optimizes two functions in conflict: geometric compactness and homogeneity to variables of a population problem, it belongs to the area of design territory. Such problems invests its utmost in the biobjetivo grouping to build groups of areas under Partitioning properties where territorial partitions must be as compact and homogeneous as possible. the resolution of compromise between two objectives must be approached with a multi-objective technique to find non-dominated solutions which in turn form the set of solutions framed in a Pareto Front. A new method is proposed to find the set of solutions not dominated based on basic aspects of order theory, particularly Hasse diagram for the Minim and computational cost management has been incorporated the metaheuristic called Variable Neighborhood Search (VNS). Finally to calibrate the parameters of VNS has been done using a factorial experiment known as Box Benhken and Response Surfaces, thus we have achieved an ideal combination of parameters to obtain satisfactory solutions to the multiobjetivo problem.