Optimal partisan districting on planar geographies

We show that optimal partisan districting in the plane with geographical constraints is an NP-complete problem

A resectorization of fire brigades in the north of Portugal

Sectorization consists of grouping the basic units of a large territory to deal with a complex problem involving different criteria. Resectorization rearranges a current sectorization avoiding substantial changes, given a set of conditions. The paper considers the case of the distribution of geographic areas of fire brigades in the north of Portugal so that they can protect and rescue the population surrounding the fire stations. Starting from a current sectorization, assuming the geographic and population characteristics of the areas and the fire brigades’ response capacity, we provide an optimized resectorization considering two objectives: to reduce the rescue time by maximizing the compactness criterion, and to avoid overload situations by maximizing the equilibrium criterion. The solution method is based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). Finally, computational results are presented and discussed.info:eu-repo/semantics/acceptedVersio

Dynamic sectorization-conceptualization and application

Sectorization is the division of a large area, territory or network into smaller parts considering one or more objectives. Dynamic sectorization deals with situations where it is convenient to discretize the time horizon in a certain number of periods. The decisions will not be isolated, and they will consider the past. The application areas are diverse and increasing due to uncertain times. This work proposes a conceptualization of dynamic sectorization and applies it to a distribution problem with variable demand. Furthermore, Genetic Algorithm is used to obtain solutions for the problem since it has several criteria; Analytical Hierarchy Process is used for the weighting procedure.info:eu-repo/semantics/acceptedVersio

Supervised regionalization methods, a survey.

This paper reviews almost four decades of contributions on the subject of supervised regionalization methods. These methods aggregate a set of areas into a predefined number of spatially contiguous regions while optimizing certain aggregation criteria. The authors present a taxonomic scheme that classifies a wide range of regionalization methods into eight groups, based on the strategy applied for satisfying the spatial contiguity constraint. The paper concludes by providing a qualitative comparison of these groups in terms of a set of certain characteristics, and by suggesting future lines of research for extending and improving these methods.regionalization, constrained clustering, analytical regions.

Zone design of specific sizes using adaptive additively weighted voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed?s weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition

Supervised regionalization methods: A survey

This paper reviews almost four decades of contributions on the subject of supervised regionalization methods. These methods aggregate a set of areas into a predefined number of spatially contiguous regions while optimizing certain aggregation criteria. The authors present a taxonomic scheme that classifies a wide range of regionalization methods into eight groups, based on the strategy applied for satisfying the spatial contiguity constraint. The paper concludes by providing a qualitative comparison of these groups in terms of a set of certain characteristics, and by suggesting future lines of research for extending and improving these methods

Estado del arte en procesos de zonificacion

Los procesos de partición espacial implican la división de un espacio geográfico en diferentes unidades o zonas según un conjunto específico de criterios. En ámbitos relacionados con las ciencias geoespaciales, la delimitación de estas zonas se realiza por agrupación de otras unidades básicas de área existentes en el espacio de trabajo. En este artículo se ofrece una revisión de los métodos de solución diseñados para este tipo de problemas, comenzando por una introducción a las técnicas heurísticas y modelos matemáticos más utilizados desde los años 60, para finalizar describiendo los recientes algoritmos aplicados a diagramas de Voronoi. También se revisan las aplicaciones en las que se han implementado algunos de estos modelos, quedando patente que son herramientas diseñadas para el tratamiento de problemas específicos, dada la dificultad de diseñar modelos genéricos y versátiles para este tipo de particiones espaciales o zonificacione

Optimal partisan districting on planar geographies

We show that optimal partisan districting and majority securing districting in the plane with geographical constraints are NP-complete problems. We provide a polynomial time algorithm for determining an optimal partisan districting for a simplified version of the problem. In addition, we give possible explanations for why finding an optimal partisan districting for real-life problems cannot be guaranteed