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Description
Facility location models are usually employed to assist decision processes in urban and regional planning. The focus of this research is extensions of a classic location problem, the Weber problem, to address continuously distributed demand as well as multiple facilities. Addressing continuous demand and multi-facilities represents major challenges. Given advances

Facility location models are usually employed to assist decision processes in urban and regional planning. The focus of this research is extensions of a classic location problem, the Weber problem, to address continuously distributed demand as well as multiple facilities. Addressing continuous demand and multi-facilities represents major challenges. Given advances in geographic information systems (GIS), computational science and associated technologies, spatial optimization provides a possibility for improved problem solution. Essential here is how to represent facilities and demand in geographic space. In one respect, spatial abstraction as discrete points is generally assumed as it simplifies model formulation and reduces computational complexity. However, errors in derived solutions are likely not negligible, especially when demand varies continuously across a region. In another respect, although mathematical functions describing continuous distributions can be employed, such theoretical surfaces are generally approximated in practice using finite spatial samples due to a lack of complete information. To this end, the dissertation first investigates the implications of continuous surface approximation and explicitly shows errors in solutions obtained from fitted demand surfaces through empirical applications. The dissertation then presents a method to improve spatial representation of continuous demand. This is based on infill asymptotic theory, which indicates that errors in fitted surfaces tend to zero as the number of sample points increases to infinity. The implication for facility location modeling is that a solution to the discrete problem with greater demand point density will approach the theoretical optimum for the continuous counterpart. Therefore, in this research discrete points are used to represent continuous demand to explore this theoretical convergence, which is less restrictive and less problem altering compared to existing alternatives. The proposed continuous representation method is further extended to develop heuristics to solve the continuous Weber and multi-Weber problems, where one or more facilities can be sited anywhere in continuous space to best serve continuously distributed demand. Two spatial optimization approaches are proposed for the two extensions of the Weber problem, respectively. The special characteristics of those approaches are that they integrate optimization techniques and GIS functionality. Empirical results highlight the advantages of the developed approaches and the importance of solution integration within GIS.
ContributorsYao, Jing (Author) / Murray, Alan T. (Thesis advisor) / Mirchandani, Pitu B. (Committee member) / Kuby, Michael J (Committee member) / Arizona State University (Publisher)
Created2012
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Description
There exist many facets of error and uncertainty in digital spatial information. As error or uncertainty will not likely ever be completely eliminated, a better understanding of its impacts is necessary. Spatial analytical approaches, in particular, must somehow address data quality issues. This can range from evaluating impacts of potential

There exist many facets of error and uncertainty in digital spatial information. As error or uncertainty will not likely ever be completely eliminated, a better understanding of its impacts is necessary. Spatial analytical approaches, in particular, must somehow address data quality issues. This can range from evaluating impacts of potential data uncertainty in planning processes that make use of methods to devising methods that explicitly account for error/uncertainty. To date, little has been done to structure methods accounting for error. This research focuses on developing methods to address geographic data uncertainty in spatial optimization. An integrated approach that characterizes uncertainty impacts by constructing and solving a new multi-objective model that explicitly incorporates facets of data uncertainty is developed. Empirical findings illustrate that the proposed approaches can be applied to evaluate the impacts of data uncertainty with statistical confidence, which moves beyond popular practices of simulating errors in data. Spatial uncertainty impacts are evaluated in two contexts: harvest scheduling and sex offender residency. Owing to the integration of spatial uncertainty, the detailed multi-objective models are more complex and computationally challenging to solve. As a result, a new multi-objective evolutionary algorithm is developed to address the computational challenges posed. The proposed algorithm incorporates problem-specific spatial knowledge to significantly enhance the capability of the evolutionary algorithm for solving the model.  
ContributorsWei, Ran (Author) / Murray, Alan T. (Thesis advisor) / Anselin, Luc (Committee member) / Rey, Segio J (Committee member) / Mack, Elizabeth A. (Committee member) / Arizona State University (Publisher)
Created2013
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Description
The shortest path between two locations is important for spatial analysis, location modeling, and wayfinding tasks. Depending on permissible movement and availability of data, the shortest path is either derived from a pre-defined transportation network or constructed in continuous space. However, continuous space movement adds substantial complexity to identifying the

The shortest path between two locations is important for spatial analysis, location modeling, and wayfinding tasks. Depending on permissible movement and availability of data, the shortest path is either derived from a pre-defined transportation network or constructed in continuous space. However, continuous space movement adds substantial complexity to identifying the shortest path as the influence of obstacles has to be considered to avoid errors and biases in a derived path. This obstacle-avoiding shortest path in continuous space has been referred to as Euclidean shortest path (ESP), and attracted the attention of many researchers. It has been proven that constructing a graph is an effective approach to limit infinite search options associated with continuous space, reducing the problem to a finite set of potential paths. To date, various methods have been developed for ESP derivation. However, their computational efficiency is limited due to fundamental limitations in graph construction. In this research, a novel algorithm is developed for efficient identification of a graph guaranteed to contain the ESP. This new approach is referred to as the convexpath algorithm, and exploits spatial knowledge and GIS functionality to efficiently construct a graph. The convexpath algorithm utilizes the notion of a convex hull to simultaneously identify relevant obstacles and construct the graph. Additionally, a spatial filtering technique based on intermediate shortest path is enhances intelligent identification of relevant obstacles. Empirical applications show that the convexpath algorithm is able to construct a graph and derive the ESP with significantly improved efficiency compared to visibility and local visibility graph approaches. Furthermore, to boost the performance of convexpath in big data environments, a parallelization approach is proposed and applied to exploit computationally intensive spatial operations of convexpath. Multicore CPU parallelization demonstrates noticeable efficiency gain over the sequential convexpath. Finally, spatial representation and approximation issues associated with raster-based approximation of the ESP are assessed. This dissertation provides a comprehensive treatment of the ESP, and details an important approach for deriving an optimal ESP in real time.
ContributorsHong, Insu (Author) / Murray, Alan T. (Thesis advisor) / Kuby, Micheal (Committee member) / Rey, Sergio (Committee member) / Arizona State University (Publisher)
Created2015