A Zero‐One Programming Model for Contiguous Land Acquisition

The land acquisition problem is a spatial partitioning problem that involves selecting multiple parcels to be acquired for a particular land use. Three selection criteria are considered: total cost, total area, and spatial contiguity. Achieving contiguity or connectivity has been problematic in previous exact methods for land acquisition. Here we present a new zero‐one programming model that enforces necessary and sufficient conditions for achieving contiguity in discrete cell landscapes, independent of other spatial attributes such as compactness. Computational experience with several demonstration problems is reported, and results and extensions are discussed.     

p‐Functional Clusters Location Problem for Detecting Spatial Clusters with Covering Approach

Regionalization or districting problems commonly require each individual spatial unit to participate exclusively in a single region or district. Although this assumption is appropriate for some regionalization problems, it is less realistic for delineating functional clusters, such as metropolitan areas and trade areas where a region does not necessarily have exclusive coverage with other regions. This paper develops a spatial optimization model for detecting functional spatial clusters, named the p‐functional clusters location problem (p‐FCLP), which has been developed based on the Covering Location Problem. By relaxing the complete and exhaustive assignment requirement, a functional cluster is delineated with the selective spatial units that have substantial spatial interaction. This model is demonstrated with applications for a functional regionalization problem using three journey‐to‐work flow datasets: (1) among the 46 counties in South Carolina, (2) the counties in the East North Central division of the US Census, and (3) all counties in the US. The computational efficiency of p‐FCLP is compared with other regionalization problems. The computational results show that detecting functional spatial clusters with contiguity constraints effectively solves problems with optimality in a mixed integer programming (MIP) approach, suggesting the ability to solve large instance applications of regionalization problems.     

Contiguity Constraints for Single‐Region Site Search Problems

This paper proposes an explicit set of constraints as a general approach to the contiguity problem in site search modeling. Site search models address the challenging problem of identifying the best area in a study region for a particular land use, given that there are no candidate sites. Criteria that commonly arise in a search include a site's area, suitability, cost, shape, and proximity to surrounding geographic features. An unsolved problem in this modeling arena is the identification of a general set of mathematical programming constraints that can guarantee a contiguous solution (site) for any 0–1 integer‐programming site search formulation. The constraints proposed herein address this problem, and we evaluate their efficacy and efficiency in the context of a regular and irregular tessellation of geographic space. An especially efficient constraint form is derived from a more general form and similarly evaluated. The results demonstrate that the proposed constraints represent a viable, general approach to the contiguity problem.     

The p‐Regions Problem. p‐区域问题

The p‐regions problem involves the aggregation or clustering of n small areas into p spatially contiguous regions while optimizing some criteria. The main objective of this article is to explore possible avenues for formulating this problem as a mixed integer‐programming (MIP) problem. The critical issue in formulating this problem is to ensure that each region is a spatially contiguous cluster of small areas. We introduce three MIP models for solving the p regions problem. Each model minimizes the sum of dissimilarities between all pairs of areas within each region while guaranteeing contiguity. Three strategies designed to ensure contiguity are presented: (1) an adaptation of the Miller, Tucker, and Zemlin tour‐breaking constraints developed for the traveling salesman problem; (2) the use of ordered‐area assignment variables based upon an extension of an approach by Cova and Church for the geographical site design problem; and (3) the use of flow constraints based upon an extension of work by Shirabe. We test the efficacy of each formulation as well as specify a strategy to reduce overall problem size.     

The Zone Definition Problem in Location-Allocation Modeling

Location-allocation modeling is a frequently used set of techniques for solving a variety of locational problems, some of which can be politically sensitive. The typical application of a location-allocation model involves locating facilities by selecting a set of sites from a larger set of candidate sites, with the selection procedure being a function of “optimality” in terms of the allocation of demand to the selected sites. In this paper we examine the sensitivity of one particular type of location-allocation model, the p-median procedure, to the definition of spatial units for which demand is measured. We show that a p-median solution is optimal only for a particular definition of spatial units and that variations in the definition of spatial units can cause large deviations in optimal facility locations. The broad implication of these findings is that the outcome of any location-allocation procedure using aggregate data should not be relied upon for planning purposes. This has important implications for a large variety of applications.     

On the Performance of the Subtour Elimination Constraints Approach for the p‐Regions Problem: A Computational Study

The p‐regions is a mixed integer programming (MIP) model for the exhaustive clustering of a set of n geographic areas into p spatially contiguous regions while minimizing measures of intraregional heterogeneity. This is an NP‐hard problem that requires a constant research of strategies to increase the size of instances that can be solved using exact optimization techniques. In this article, we explore the benefits of an iterative process that begins by solving the relaxed version of the p‐regions that removes the constraints that guarantee the spatial contiguity of the regions. Then, additional constraints are incorporated iteratively to solve spatial discontinuities in the regions. In particular we explore the relationship between the level of spatial autocorrelation of the aggregation variable and the benefits obtained from this iterative process. The results show that high levels of spatial autocorrelation reduce computational times because the spatial patterns tend to create spatially contiguous regions. However, we found that the greatest benefits are obtained in two situations: (1) when ; and (2) when the parameter p is close to the number of clusters in the spatial pattern of the aggregation variable.     

EFFICIENT ALGORITHMS FOR CONSTRUCTING PROPER HIGHER ORDER SPATIAL LAG OPERATORS*

ABSTRACT. This paper extends the work of Blommestein and Koper (1992)–BK–on the construction of higher-order spatial lag operators without redundant and circular paths. For the case most relevant in spatial econometrics and spatial statistics, i.e., when contiguity between two observations (locations) is defined in a simple binary fashion, some deficiencies of the BK algorithms are outlined, corrected and an improvement suggested. In addition, three new algorithms are introduced and compared in terms of performance for a number of empirical contiguity structures. Particular attention is paid to a graph theoretic perspective on spatial lag operators and to the most efficient data structures for the storage and manipulation of spatial lags. The new forward iterative algorithm which uses a list form rather than a matrix to store the spatial lag information is shown to be several orders of magnitude faster than the BK solution. This allows the computation of proper higher-order spatial lags “on the fly” for even moderately large data sets such as 3,111 contiguous U. S. counties, which is not practical with the other algorithms.     

An Evolutionary Algorithm for Site Search Problems

The goal of solving a site search problem is to allocate a contiguous set of land parcels such that the total land acquisition cost, or other objectives, are optimized. This article describes the design and implementation of an evolutionary algorithm (EA) that can be used to solve site search problems. In this article, a graph representation is used to define the spatial structure of solutions to the problem. By using this representation, the contiguity of a site is maintained during the initialization, mutation, and local search operations of the EA. The effectiveness of the EA in finding optimal or near-optimal solutions is demonstrated by testing it on a series of problems whose optimal solutions are known.     

甘肃经济空间结构的现状、问题与战略选择

区域经济空间结构和产业结构一样是不断发展变化的经济结构,具有向合理化和高级化变化的趋势。本文从区域经济空间结构要素的角度详细的考察了甘肃城市体系、交通体系和经济集中区的情况。其次,重点分析了甘肃经济空间结构的特征及其问题,得出了许多有意义的结论。最后,通过把区域经济空间结构理论与甘肃具体省情相结合,提出了甘肃"大十字"经济空间结构的发展战略,同时分析了实施这种发展战略的意义。     

A Spatial Prior for Bayesian Vector Autoregressive Models

In this paper we develop a Bayesian prior motivated by cross-sectional spatial autoregressive models for use in time-series vector autoregressive forecasting involving spatial variables. We compare forecast accuracy of the proposed spatial prior to that from a vector autoregressive model relying on the Minnesota prior and find a significant improvement. In addition to a spatially motivated prior variance as in LeSage and Pan (1995) we develop a set of prior means based on spatial contiguity. A Theil-Goldberger estimator may be used for the proposed model making it easy to implement.     

Adaptive Cell Tower Location Using Geostatistics. 基于地统计学的适应性基站发射塔选址研究

In this article, we address the problem of allocating an additional cell tower (or a set of towers) to an existing cellular network, maximizing the call completion probability. Our approach is derived from the adaptive spatial sampling problem using kriging, capitalizing on spatial correlation between cell phone signal strength data points and accounting for terrain morphology. Cell phone demand is reflected by population counts in the form of weights. The objective function, which is the weighted call completion probability, is highly nonlinear and complex (nondifferentiable and discontinuous). Sequential and simultaneous discrete optimization techniques are presented, and heuristics such as simulated annealing and Nelder–Mead are suggested to solve our problem. The adaptive spatial sampling problem is defined and related to the additional facility location problem. The approach is illustrated using data on cell phone call completion probability in a rural region of Erie County in western New York, and accounts for terrain variation using a line‐of‐sight approach. Finally, the computational results of sequential and simultaneous approaches are compared. Our model is also applicable to other facility location problems that aim to minimize the uncertainty associated with a customer visiting a new facility that has been added to an existing set of facilities.     

济南都市圈城市化空间分异特征及其引导策略

随着快速城市化的发展,都市圈成为我国大城市功能地域组织的重要形式。本文对济南都市圈城市化发展的空间分异特征和问题进行了分析,发现济南都市圈中虽然济南具有较高的集聚规模,但却缺乏相应的辐射带动能力,圈内多数县域尤其是黄河以北地区城市化滞后,加之其它中心城市实力不够强大,严重阻碍了济南及其都市圈竞争优势的发挥。由此提出了"强化核心、多元中心、区域联动、县域支撑"的城市化空间布局策略,并以城乡土地资源合理利用为核心,分别就土地分类管制和分区引导等两方面城市化协调引导机制进行了探讨。     

Constructing the Spatial Weights Matrix Using a Local Statistic

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W , based on the principle that spatial structure should be considered in a two‐part framework, those units that evoke a distance effect, and those that do not. Our two‐variable local statistics model (LSM) is based on the G_i* local statistic. The local statistic concept depends on the designation of a critical distance, d_c, defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well‐known spatial weights matrix specifications—two different contiguity configurations, three different inverse distance formulations, and three semi‐variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran's I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.     

Using Linear Integer Programming for Multi‐Site Land‐Use Allocation

Research in the area of spatial decision support (SDS) and resource allocation has recently generated increased attention for integrating optimization techniques with GIS. In this paper we address the use of spatial optimization techniques for solving multi‐site land‐use allocation (MLUA) problems, where MLUA refers to the optimal allocation of multiple sites of different land uses to an area. We solve an MLUA problem using four different integer programs (IP), of which three are linear integer programs. The IPs are formulated for a raster‐based GIS environment and are designed to minimize development costs and to maximize compactness of the allocated land use. The preference for either minimizing costs or maximizing compactness has been made operational by including a weighting factor. The IPs are evaluated on their speed and their efficacy for handling large databases. All four IPs yielded the optimal solution within a reasonable amount of time, for an area of 8 × 8 cells. The fastest model was successfully applied to a case study involving an area of 30 × 30 cells. The case study demonstrates the practical use of linear IPs for spatial decision support issues.     

A Programming Approach to Minimizing and Maximizing Spatial Autocorrelation Statistics

A programming approach is presented for identifying the form of the weights matrix W which either minimizes or maximizes the value of Moran's spatial autocorrelation statistic for a specified vector of data values. Both nonlinear and linear programming solutions are presented. The former are necessary when the sum of the links in W is unspecified while the latter can be used if this sum is fixed. The approach is illustrated using data examined in previous studies for two variables measured for the counties of Eire. While programming solutions involving different sets of constraints are derived, all yield solutions in which the number of nonzero elements in W is considerably smaller than that in W defined using the contiguity relationships between the counties. In graph theory terms, all of the Ws derived define multicomponent graphs. Other characteristics of the derived Ws are also presented.     

Model Uncertainty in Matrix Exponential Spatial Growth Regression Models

This article considers the most important aspects of model uncertainty for spatial regression models, namely, the appropriate spatial weight matrix to be employed and the appropriate explanatory variables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used in the regional growth literature, and develop a simple Bayesian model‐averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on previous work by reducing the computational costs through the use of Bayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial Durbin matrix exponential model has theoretical and computational advantages over the spatial autoregressive specification due to the ease of inversion, differentiation, and integration of the matrix exponential. In particular, the matrix exponential has a simple matrix determinant that vanishes for the case of a spatial weight matrix with a trace of zero. This allows for a larger domain of spatial growth regression models to be analyzed with this approach, including models based on different classes of spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants and three classes of spatial weight matrices (contiguity‐based, k‐nearest neighbor, and distance‐based spatial weight matrices), using a data set of income per capita growth for 273 European regions.     

Ethnology And Historical Geography (Landscape and Ethnos,XIII)

The theory that ethnogenesis is triggered by bursts of innate ethnic drive or energy, following an incubation period, is examined further. An examination of the historical record suggests that several superethnoses may arise simultaneously in various parts of the world. The regions covered by such superethnoses may be broken up by natural barriers ruling out any exchange of population or cultural influences, and yet the regions involved in such energetic surges tend to be monolithic. The spatial contiguity of bursts of ethnic energy at particular periods in history is illustrated by a number of examples ranging from Europe to the Far East, but what precisely triggers these energetic displays still requires the formulation of a hypothesis.     

The Majority Theorem for the Single (p = 1) Median Problem and Local Spatial Autocorrelation

Except for about a half dozen papers, virtually all (co)authored by Griffith, the existing literature lacks much content about the interface between spatial optimization, a popular form of geographic analysis, and spatial autocorrelation, a fundamental property of georeferenced data. The popular p-median location-allocation problem highlights this situation: the empirical geographic distribution of demand virtually always exhibits positive spatial autocorrelation. This property of geospatial data offers additional overlooked information for solving such spatial optimization problems when it actually relates to their solutions. With a proof-of-concept outlook, this paper articulates connections between the well-known Majority Theorem of the 1-median minisum problem and local indices of spatial autocorrelation; the LISA statistics appear to be the more useful of these later statistics because they better embrace negative spatial autocorrelation. The relationship articulation outlined here results in the positing of a new proposition labeled the egalitarian theorem.