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

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.

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

Strategic districting for the mitigation of educational segregation : a pilot model for school district optimization in Helsinki

Helsingin kaupunkirakenne on eriytynyt viimeisten vuosikymmenien aikana merkittävästi sosiaalisilla mittareilla tarkasteltuna. Kehitys on heijastunut kouluihin oppilaspohjien ja oppimistuloksien erojen kasvuna, minkä lisäksi Helsingissä on löydetty viitteitä myös itsenäisistä kouluvaikutuksista. Koulujen eriytymiskehityksen pelätään mainevaikutuksen kautta kiihdyttävän alueellista segregaatiota ja siten oppilaspohjien eriytymistä entisestään. Oppilaspohjien eroihin on kuitenkin mahdollista vaikuttaa määrittämällä oppilasalueet uudelleen tavalla, joka minimoi oppilasalueiden välisiä sosiaalisia eroja mahdollisimman tehokkaasti. Tätä varten tarvitaan uudenlaisia, koneoppimiseen perustuvia optimointityökaluja. Tämän opinnäytetyön päätavoitteena on tutkia mahdollisuutta optimoida Helsingin oppilasalueita väestöpohjiltaan sisäisesti heterogeenisemmiksi ja keskenään homogeenisemmiksi. Tavoitetta varten olen kehittänyt työssäni automatisoidun optimointimallin, joka minimoi sosiaalisten muuttujien varianssia oppilasalueiden välillä oppilasalueiden muotoa varioimalla. Mallin pilottisovelluksessa optimoin Helsingin oppilaaksiottoalueita tasaisemmiksi käyttäen optimoitavana muuttujana vieraskielisen väestön osuutta. Olemassa olevaa kouluverkostoa eli koulujen sijaintia, oppilasalueiden maantieteellistä yhtenäisyyttä, enimmäisoppilasmääriä koulukohtaisella marginaalilla sekä koulukohtaista koulumatkan enimmäispituutta on käytetty mallissa alueiden muodostamista rajoittavina tekijöinä. Tutkimukseni keskeinen löydös on, että oppilasaluerajoja siirtelemällä oppilasalueiden sosiaalisen pohjan eroihin voidaan vaikuttaa Helsingissä merkittävästi. Malli vaatii kuitenkin vielä perusteellista jatkokehittämistä soveltuakseen aluejakojen käytännön suunnitteluun, ja tässä vaiheessa sen merkittävimmät kehityskohteet liittyvät optimoitujen alueiden muotoon, mallin laskennalliseen vaativuuteen ja koulumatkojen turvallisuutta mittaavan optimointiparametrin puuttumiseen.The social urban structure of Helsinki has experienced a significant rise in spatial differences during the last two decades. This development has reflected on schools as rising differences between schools’ student compositions and learning outcomes. Additionally, signs of independent school effects have been observed in several studies. The differentiation of student compositions is feared to exacerbate residential segregation and differentiate schools’ operating environments further. It is possible, however, to intervene this development by drawing the school attendance districts such that the social differences between schools’ student compositions are effectively minimized. For this purpose, new machine learning based optimization tools are needed. The main objective of this master’s thesis study is to examine the possibility to optimize Helsinki’s school districts toward more internally heterogeneous and externally homogeneous social compositions. For this purpose, I have developed an optimization model that minimizes the variance of social variables between school districts by iteratively redrawing the districts’ borders. In a pilot application of the model I optimize the school districts of Helsinki by using the share of population with immigrant background as the optimization variable, while existing school infrastructure (the school locations and student capacities), spatial contiguity of the districts, and school-specific maximum travel distances are used as constraints restricting the shapes that the districts can take. The core finding of this study is that in Helsinki, the social compositions of school districts can be significantly evened out by redrawing the school district borders. However, for the model to be suitable for district planning in practice it needs further development. At this stage, the main limitations of the model are related to the shapes of the optimized districts, the model’s time complexity and the lack of a constraint or optimization parameter that accounts for the safety of children’s school trips

A Computer-Aided Decision Support System for Making Locational Decisions, 1990

This report is the product of a first-year research project in the University Transportation Centers Program. This project was carried out by an interdisciplinary research team at The University of Iowa's Public Policy Center. The project developed a computerized system to support decisions on locating facilities that serve rural areas while minimizing transportation costs. The system integrates transportation databases with algorithms that specify efficient locations and allocate demand efficiently to service regions; the results of these algorithms are used interactively by decision makers. The authors developed documentation for the system so that others could apply it to estimate the transportation and route requirements of alternative locations and identify locations that meet certain criteria with the least cost. The system was developed and tested on two transportation-related problems in Iowa, and this report uses these applications to illustrate how the system can be used

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

Authoritative and Unbiased Responses to Geographic Queries

Trust in information systems stem from two key properties of responses to queries regarding the state of the system, viz., i) authoritativeness, and ii) unbiasedness. That the response is authoritative implies that i) the provider (source) of the response, and ii) the chain of delegations through which the provider obtained the authority to respond, can be verified. The property of unbiasedness implies that no system data relevant to the query is deliberately or accidentally suppressed. The need for guaranteeing these two important properties stem from the impracticality for the verifier to exhaustively verify the correctness of every system process, and the integrity of the platform on which system processes are executed. For instance, the integrity of a process may be jeopardized by i) bugs (attacks) in computing hardware like Random Access Memory (RAM), input/output channels (I/O), and Central Processing Unit( CPU), ii) exploitable defects in an operating system, iii) logical bugs in program implementation, and iv) a wide range of other embedded malfunctions, among others. A first step in ensuing AU properties of geographic queries is the need to ensure AU responses to a specific type of geographic query, viz., point-location. The focus of this dissertation is on strategies to leverage assured point-location, for i) ensuring authoritativeness and unbiasedness (AU) of responses to a wide range of geographic queries; and ii) useful applications like Secure Queryable Dynamic Maps (SQDM) and trustworthy redistricting protocol. The specific strategies used for guaranteeing AU properties of geographic services include i) use of novel Merkle-hash tree- based data structures, and ii) blockchain networks to guarantee the integrity of the processes