A Balancing Proposal for Population Variables in Multiobjective Problems: Towards Pareto’s Frontier for Homogeneity

Abstract

Clustering is one of the most successful techniques for territorial design, location-allocation problems etc. In this type of problems, the parameters are usually optimized by means of a single objective. However, real applications are far from being solved without the application of multi-objective approaches. In this paper we present a bi-objective partitioning proposal to solve problems that involve census-based variables for territorial design (TD), known to be a high complexity computational problems. Two quality measures for partitioning are chosen, which are simultaneously optimized. The first quality measure obeys a geometrical concept of distances, whereas the second measure focuses in the calculation of balance for a descriptive variable. A formulation is included with a flexible notation for the second objective about variable population and this is our main contribution. Furthermore, our model allows for implementations in several languages and it is possible to reach quality solutions within a reasonable computation time.

Experimental tests show that it is possible to get results in the Pareto frontier, which is constructed with the approximate solutions generated by the chosen metaheuristic. In this case, one pilot test and its associated Pareto’s front, is presented. These solutions are non-dominated and non-comparable with a similar mechanism on which the minima of a Hasse Diagram are reached.