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

Spatial Optimization Methods And System For Redistricting Problems

Redistricting is the process of dividing space into districts or zones while optimizing a set of spatial criteria under certain constraints. Example applications of redistricting include political redistricting, school redistricting, business service planning, and city management, among many others. Redistricting is a mission-critical component in operating governments and businesses alike. In research fields, redistricting (or region building) are also widely used, such as climate zoning, traffic zone analysis, and complex network analysis. However, as a combinatorial optimization problem, redistricting optimization remains one of the most difficult research challenges. There are currently few automated redistricting methods that have the optimization capability to produce solutions that meet practical needs. The absence of effective and efficient computational approaches for redistricting makes it extremely time-consuming and difficult for an individual person to consider multiple criteria/constraints and manually create solutions using a trial-and-error approach. To address both the scientific and practical challenges in solving real-world redistricting problems, this research advances the methodology and application of redistricting by developing a new computational spatial optimization method and a system platform that can address a wide range of redistricting problems, in an automated and computation-assisted manner. The research has three main contributions. First, an efficient and effective spatial optimization method is developed for redistricting. The new method is based on a spatially constrained and Tabu-based heuristics, which can optimize multiple criteria under multiple constraints to construct high-quality optimization solutions. The new approach is evaluated with real-world redistricting applications and compared with existing methods. Evaluation results show that the new optimization algorithm is more efficient (being able to allow real-time user interaction), more flexible (considering multiple user-expressed criteria and constraints), and more powerful (in terms of optimization quality) than existing methods. As such, it has the potential to enable general users to perform complex redistricting tasks. Second, a redistricting system, iRedistrict, is developed based on the newly developed spatial optimization method to provide user-friendly visual interface for defining redistricting problems, incorporating domain knowledge, configuring optimization criteria and methodology parameters, and ultimately meeting the needs of real-world applications for tackling complex redistricting tasks. It is particularly useful for users of different skill levels, including researchers, practitioners, and the general public, and thus enables public participation in challenging redistricting tasks that are of immense public interest. Performance evaluations with real-world case studies are carried out. Further computational strategies are developed and implemented to handle large datasets. Third, the newly developed spatial optimization method is extended to solve a different spatial optimization problem, i.e., spatial community structure detection in complex networks, which is to partition networks to discover spatial communities by optimizing an objective function. Moreover, a series of new evaluations are carried out with synthetic datasets. This set of evaluations is different from the previous evaluations with case studies in that, the optimal solution is known with synthetic data and therefore it is possible to evaluate (1) whether the optimization method can discover the true pattern (global optima), and (2) how different data characteristics may affect the performance of the method. Evaluation results reveal that existing non-spatial methods are not robust in detecting spatial community structure, which may produce dramatically different outcomes for the same data with different characteristics, such as different spatial aggregations, sampling rates, or noise levels. The new optimization method with spatial constraints is significantly more stable and consistent. In addition to evaluations with synthetic datasets, a case study is also carried out to detect urban community structure with human movements, to demonstrate the application and effectiveness of the approach

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

Healthcare Districting Optimization Using Gray Wolf Optimizer and Ant Lion Optimizer Algorithms (case study: South Khorasan Healthcare System in Iran)

In this paper, the problem of population districting in the health system of South Khorasan province has been investigated in the form of an optimization problem. Now that the districting problem is considered as a strategic matter, it is vital to obtain efficient solutions in order to implement in the system. Therefore in this study two meta-heuristic algorithms, Ant Lion Optimizer (ALO) and Grey Wolf Optimizer (GWO), have been applied to solve the problem in the dimensions of the real world. The objective function of the problem is to maximize the population balance in each district. Problem constraints include unique assignment as well as non-existent allocation of abnormalities. Abnormal allocation means compactness, lack of contiguous, and absence of holes in the districts. According to the obtained results, GWO has a higher level of performance than the ALO. The results of this problem can be applied as a useful scientific tool for districting in other organizations and fields of application

CLUSTERING OF TERRITORIAL AREAS: A MULTI-CRITERIA DISTRICTING PROBLEM

Endogenous resources, economic profile and socio-economic issues are the criteria that define the development level and the identity features of a territorial unit. The territorial units that organize the country, in political and administrative terms – parishes and counties –, have a hierarquical structure, which initially reflected the organization of productive activities as well as the tradition State organization. The success of development policies addressed to territorial agglomerates depends on its homogeneity and of their territorial units. Facing to this the clustering of territorial areas can be stated as a districting multi-criteria problem. Thus, this paper aims to propose a framework for obtaining homogenous territorial clusters based on a Pareto frontier that includes multicriteria related to the territorial endogenous resources, economic profile and sociocultural features. This framework is developed in two phases. First, the criteria correlated with the development at the territory unit level are determined through statistical and econometric methods. Then, a multi-criteria approach is developed to allocate each territory unit to an agglomerate of territory according to the Pareto frontier established. The framework is applied to the context of a set of parishes and counties of the Alentejo Central region, southern Portugal. Results are presented and discussed in the scope of a regional strategy of development

Uso de diferentes algoritmos de otimização para definição de áreas de serviço de esquadras de polícia para Portugal

Dissertation presented as the partial requirement for obtaining a Master's degree in Geographic Information Systems and ScienceA segurança é considerada um direito fundamental nos estados democráticos. É uma condição que exige cada vez mais ferramentas avançadas de análise espacial, para apoiar a adequação de recursos e a disposição espacial das forças de segurança. A reorganização das forças de segurança no contexto atual depende da distribuição da população e do seu dinamismo. O processo de agrupar pequenas áreas geográficas para formar as áreas de serviço é designado por districting. Esta dissertação tem como objetivo a otimização espacial das forças de segurança tendo em consideração a distribuição espacial da população residente do distrito administrativo de Setúbal. A análise de dados da população residente foi efetuada com a análise hot spot para estudar a sua distribuição ao nível da freguesia. Implementou-se um algoritmo genético e efetuaram-se testes experimentais com os dados da população residente e dos grupos vulneráveis, para criar áreas de serviço das esquadras de polícia. Compararam-se os resultados obtidos com o Automatic Zoning Procedure – Simulated Annealing (AZP-SA) utilizando os mesmos dados. A população do distrito concentra-se sobretudo na península de Setúbal, existindo uma grande assimetria na sua distribuição geográfica. Os testes experimentais com o algoritmo genético demonstram que as áreas de serviço criadas, apresentam uma soma das diferenças da população com uma grande variação. O AZP-SA obteve um desempenho ligeiramente superior ao algoritmo genético implementado. A implementação do algoritmo permitiu obter soluções de áreas de serviço, no entanto, o desempenho do AZP-SA foi ligeiramente superior. A grande assimetria da população do distrito administrativo de Setúbal dificultou a criação de áreas de serviço mais equitativas.Security is to consider being a fundamental right in democratic societies. It is a condition that requires advanced spatial analysis tools to support security forces in the spatial disposition and adequacy of resources. Nowadays security forces reorganization, depends on the population distribution and dynamic. Districting is the process of grouping small geographic areas in service areas. The main objective of this thesis is the spatial optimization of security forces considering the spatial disposition of the population in Setubal administrative district. Data analysis was done with the hot spot analysis to study the population and their distribution at freguesia level. A genetic algorithm was implemented to create service areas and experimental tests were performed with the population data and vulnerable groups. We compared the results with the Automatic Zoning Procedure - Simulated Annealing (AZP-SA). The population concentrates in Setubal peninsula denoting a great asymmetry on their geographical distribution. Experimental tests with the genetic algorithm show a large variation of a sum of the population differences in service areas. AZP-SA performed better than the genetic algorithm. The solutions for the service areas were obtained with the genetic algorithm. However, the performance of AZP-SA is slightly higher. The difficult to obtain equitable areas is due the great asymmetry of the population

An overview of neighbourhood search metaheuristics

This paper gives details of the steps needed to undertake neighbourhood search for a combinatorial optimization problem. The main variations are briefly described and pointers for future research briefly discussed. Throughout there is extensive referencing to some of the most important publications in the are

The Politico-Economics of Electricity Planning in Developing Countries : A Case Study of Ghana

The first author would like to thank the University of Aberdeen and the Henderson Economics Research Fund for funding his PhD studies in the period 2011-2014 which formed the basis for the research presented in this paper.Peer reviewedPostprin

Districting Problems - New Geometrically Motivated Approaches

This thesis focuses on districting problems were the basic areas are represented by points or lines. In the context of points, it presents approaches that utilize the problem\u27s underlying geometrical information. For lines it introduces an algorithm combining features of geometric approaches, tabu search, and adaptive randomized neighborhood search that includes the routing distances explicitly. Moreover, this thesis summarizes, compares and enhances existing compactness measures

Chemical reaction optimization for the set covering problem

The set covering problem (SCP) is one of the representative combinatorial optimization problems, having many practical applications. This paper investigates the development of an algorithm to solve SCP by employing chemical reaction optimization (CRO), a general-purpose metaheuristic. It is tested on a wide range of benchmark instances of SCP. The simulation results indicate that this algorithm gives outstanding performance compared with other heuristics and metaheuristics in solving SCP. © 2014 IEEE.postprin