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Distance is one of the most important concepts in geography and spatial analysis. Since distance calculation is straightforward for points, measuring distances for non-point objects often involves abstracting them into their representative points. For example, a polygon is often abstracted into its centroid, and the distance from/to the polygon is then measured using the centroid. Despite the wide use of representative points to measure distances of non-point objects, a recent study has shown that such a practice might be problematic and lead to biased coefficient estimates in regression analysis. The study proposed a new polygon-to-point distance metric, along with two computation algorithms. However, the efficiency of these distance calculation algorithms is low. This research provides three new methods, including the random point-based method, polygon partitioning method, and axis-aligned minimum areal bounding box-based (MABB-based) method, to compute the new distance metric. Tests are provided to compare the accuracy and computational efficiency of the new algorithms. The test results show that each of the three new methods has its advantages: the random point-based method is easy to implement, the polygon partitioning method is most accurate, and the MABB-based method is computationally efficient. [ABSTRACT FROM AUTHOR]

Abstract: The p‐median problem (PMP) is one of the most applied location problems in urban and regional planning. As an NP‐hard problem, the PMP remains challenging to solve optimally, especially for large‐sized problems. A number of heuristics have been developed to obtain PMP solutions in a fast manner. Among the heuristics, the Teitz and Bart (TB) algorithm has been found effective for finding high‐quality solutions. In this article, we present a spatial‐knowledge‐enhanced Teitz and Bart (STB) heuristic method for solving PMPs. The STB heuristic prioritizes candidate facility sites to be examined in the solution set based on the spatial distribution of demand and service provision. Tests based on a range of PMPs demonstrate the effectiveness of the STB heuristic. This new algorithm can be incorporated into current commercial GIS packages to solve a wide range of location‐allocation problems. [ABSTRACT FROM AUTHOR]

Analysis results are often found to vary with the way we abstract geographical space. When continuous geographic phenomena are abstracted, processed, and stored in a digital environment, some level of discretization is often employed. Information loss in a discretization process brings about uncertainty/error, and as a result research findings may be highly dependent on the particular discretization method used. This article examines one spatial problem concerning how to achieve the maximal regional coverage given a limited number of service facilities. Two widely used geographical space abstraction approaches are examined, the point-based representation and the area-based representation, and issues associated with each representation scheme are analyzed. To accommodate the limitations of the existing representation schemes, a mixed representation strategy is proposed along with a new maximal covering model. Experiments are conducted to site warning sirens in Dublin, Ohio. Results demonstrate the effectiveness of the mixed representation scheme in finding high-quality solutions when the regional coverage level is medium or high. [ABSTRACT FROM AUTHOR]

The current method for delineating U. S. metropolitan and micropolitan statistical areas (collectively referred to as core-based statistical areas- CBSAs) is to cluster counties based on the strength of commuting interactions between outlying areas and urban cores. The social and economic integration of a metropolitan or a micropolitan statistical area is operationalized using what we believe is an outdated, monocentric perspective on functional spatial structure: one that fixates solely on inward and reverse commuting. We propose a new spatial optimization model for delineating CBSAs that can better account for polycentric urban structure by considering all intercounty commuting linkages. Our model seeks to find the boundaries that maximize the containment of entire webs of intra- CBSA intercounty commuting. We apply the proposed method to delineate alternative sets of metropolitan and micropolitan statistical areas for comparison with the federal government's currently defined (2010 Office of Management and Budget [ OMB] standards) official CBSAs. El método actual para delimitar áreas estadísticas micropolitanas y metropolitana en los Estados Unidos (denomidado genéricamente áreas estadísticos nucleares o core-statistical areas- CBSA) consiste en agrupar condados en base a la fuerza de las interacciones de los desplazamientos residencia-trabajo entre las zonas periféricas y los núcleos urbanos. La integración social y económica de un área estadística metro y micro politana se pone en operación usando un enfoque funcional que los autores consideran obsoleto que se basa en una estructura espacial urbana monocéntrica. Dicho enfoque se limita únicamente a los desplazamientos hacia el interior y de vuelta. Los autores proponen un nuevo modelo de optimización espacial para delinear CBSAs que respresenta mejor una estructura urbana policéntrica que considera todos los desplazamientos entre condados. El modelo busca encontrar los límites que maximizan la inclusión de redes enteras de desplazamientos intra CBSA y entre condados. El método propuesto es aplicado para delinear conjuntos alternativos de áreas estadísticas metropolitanas y micropolitanas y es comparado con los límites oficiales actuales de CBSA proporcionados por gobierno federal (de acuerdo a los lineamientos de la Oficina de Administración y Presupuesto u Office of Management Budget-OMB) en 2010). 目前用于描述美国大都市区与居住区统计区域（共同地被称为基于核心的统计区域-CBSAs）的方法，主要是基于边远地区和城市核心区间的相互作用强度对郡县进行聚类。大都市区或居住区统计区域社会与经济一体化的运作方式，采用的是一种功能空间结构上落伍的单中心视角，即仅关注内部交换或反向交换。本文提出了一种新的空间优化模型用于描述CBSAs，将所有内部通勤联系考虑在内，能更好地解释多中心城市结构。该模型力图发现能最大化包含内部CBSA通勤联系网的边界。最后，将该模型应用于大都市区和居住区的统计区域描述，并与联邦政府目前定义的官方CBSAs（管理与预算 [OMB]标准2010办公室）进行了对比研究。 [ABSTRACT FROM AUTHOR]

This article discusses spatial optimization in geography, focusing on contributions of geographers in explicit geographical contexts. An overview of spatial optimization is given, as well as illustrative examples. Many of the individuals contributing to this area of the discipline are identified, demonstrating the breadth of academic institutions spanning the globe where spatial optimization is represented in the research and curriculum of geographers. The article provides a characterization of what a spatial optimization problem is, but also properties, relationships, and challenges behind this. The ultimate purpose of this article is to highlight the spatial optimization subspecialty within geography and in doing so, highlight the need for continued spatial model development and application in the discipline. Further, there is also a need for research focused on techniques to solve spatial optimization problems, particularly in the context of geographic information systems. [ABSTRACT FROM PUBLISHER]

Uncertainties and errors associated with aggregation have long been recognized in the study of spatial problems. In facility location modeling, while much has been done to examine the aggregation of large datasets of discrete points, errors and uncertainties involved in aggregating continuous spatial units are not well understood. This study focuses on the effects of aggregating continuous spatial units into discrete points within the context of the location set covering problem. We propose new measures to understand and quantify errors associated with a continuous aggregation scheme. In a real-world application, the proposed methods can be used to suggest an appropriate aggregation scheme before the application of the location model. We demonstrate the concepts developed here with an empirical study of siting emergency warning sirens in the city of Dublin, OH. [ABSTRACT FROM PUBLISHER]