A bi-objective model for territorial design

Abstract

The clustering of spatial-geographic units, zones or areas has been used to solve problems related to Territorial Design. Clustering adapts to the definition of territorial design for a specific problem, which demands spatial data processing under clustering schemes with topological requirements for the zones. For small sized instances, once the geographical compactness is attended to as an objective function, this problem has been solved by exact methods with an acceptable response time. However, for larger instances and due to the combinatory nature of this problem, the computational complexity increases and the use of approximated methods becomes a necessity, in such a way that when geographical compactness was the only cost function a couple of approximated methods were incorporated giving satisfactory results. A particular case of this kind of problems that has had our attention in recent years is the classification by partitioning of AGEBs (Basic Geographical Units by its initials in Spanish). Some work has been made related to the formation of compact groups of AGEBs, but additional re-strictions were often not considered. A very interesting and highly demanded application problem is to extend the compact clustering to form groups with for some of its descriptive variables. This problem translates to a multi-objective approach that has to pursue two objectives to attain a balance between them. At this point, to reach a set of non-dominated and non-comparable solutions, a method has been included that allows obtaining the Pareto front through the Hasse diagram, which implies proposing a mathematical programming model and the synthetic resulting between compactness and homogeneity.