海湾型半城市化地区空间形态演化模拟

元胞自动机（CA）是模拟城市土地利用演变过程的有效工具,转换规则和元胞邻域是元胞模型的核心。综合考虑元胞邻域的距离衰减效应,基于模拟退火算法（SA）挖掘最优的转换规则,文章构建了一种考虑邻域衰减的城市演化模型（SA-NDCA）。模型以负幂指数函数作为元胞邻域的衰减曲线表示元胞邻域的距离衰减效应;运用模拟退火优化算法计算城市CA模型模拟结果与样本点的累积差异,在目标解空间快速搜索以提取最优的转换规则;最后以厦门市半城市化地区为研究案例,模拟了研究区域1995―2010年期间的城市空间形态演化,通过混淆矩阵和Kappa系数评价了模型的模拟精度,1995―2010年期间的建设用地模拟精度为68.5%,总体精度达到86.2%,Kappa系数达到66.3,取得了较好的模拟效果。利用提出的SA-NDCA模型,成功模拟了研究区2010―2020年期间的城市空间形态演化,结果显示,所预测的演化情景与中国当前实施的新型城镇化战略十分契合。     

A bat-inspired approach to define transition rules for a cellular automaton model used to simulate urban expansion

A new metaheuristic approach is presented to discover transition rules for a cellular automaton (CA) model using a novel bat movement algorithm (BA). CA is capable of simulating the evolution of complex geographical phenomena, and transition rules lie at the core of these models. An intelligence algorithm based on the echolocation behavior of bats is used to discover explicit transition rules for use in simulating urban expansion. CA transition rules are formed by links between attribute constraint items and classification items. The transition rules are derived using the BA to optimize the lower and upper threshold values for each attribute. The BA-CA model is then constructed for the simulation of urban expansion observed for Nanjing City, China. The total accuracy of newly formulated BA-CA model for this application is 86.9%, and the kappa coefficient is 0.736, which strongly suggest that the interactions of bats are effective in capturing the relationships between spatial variables and urban dynamics. It is further demonstrated that this bat-inspired BA-CA model performs better than the null model, the particle swarm optimization-based CA model (PSO-CA), and the ant colony optimization-based CA model (ACO-CA) using the same dataset. The model validation and comparison illustrate the novel capability of BA for discovering transition rules of CA during the simulation of urban expansion and potentially for other geographic phenomena.     

Optimal rural land use allocation in central China: Linking the effect of spatiotemporal patterns and policy interventions

Rural land use development is experiencing a transition stage of socioeconomic and land use development in China. Historic land use transition process and policy interventions have key influence on the applicability of land use allocation solutions in future land use management. Strategic land use allocation is therefore required to possess a good adjustment capability to the transition process. Although heuristic optimization methods have been promising to solve land use allocation problems, most of them ignored the spatially explicit effect of historic land use transition and policies. To help resolve this issue, this study aims to optimize future land use pattern in the context of rural land use development. We took Yunmeng County, one of the typical major grain producing and rapidly urbanizing areas in central China, as a case study and solved the sustainable land use allocation problem by using an improved heuristic optimization model. The model was constructed based on the integration of a spatial discrete particle swarm optimization and cellular automata-Markov simulation approach. The spatiotemporal land use patterns and policy interventions were represented by the CA-Markov as in spatially explicit transition rules, and then incorporated into the discrete PSO for optimal land use solutions. We examined the influence of the joint effect of spatiotemporal land use patterns and policy interventions on the land use allocation outcome. Our results demonstrate the robustness and potential of the proposed model, and, more importantly, indicate the significance of incorporating the spatiotemporal land use patterns and policy interventions into rural land use allocation.     

基于粗集的知识发现与地理模拟——以深圳市土地利用变化为例

为了更有效地模拟地理现象的复杂演变过程,提出了用粗集理论来确定元胞自动机 (CA)不确定性转换规则的新方法。CA可以通过局部规则来有效地模拟许多地理现象的演变过程。但目前缺乏很好定义CA转换规则的方法。往往采用启发式的方法来定义CA的转换规则,这些转换规则是静态的,而且其参数值多是确定的。在反映诸如城市扩张、疾病扩散等不确定性复杂现象时,具有一定的局限性。利用粗集从GIS和遥感数据中发现知识,自动寻找CA的不确定性转换规则,基于粗集的CA在缩短建模时间的同时,能提取非确定性的转换规则,更好地反映复杂系统的特点。采用所提出的方法模拟了深圳市的城市发展过程,取得了比传统MCE方法更好的模拟效果。     

Calibrating a Land Parcel Cellular Automaton (LP-CA) for urban growth simulation based on ensemble learning

The reliability of raster cellular automaton (CA) models for fine-scale land change simulations has been increasingly questioned, because regular pixels/grids cannot precisely represent irregular geographical entities and their interactions. Vector CA models can address these deficiencies due to the ability of the vector data structure to represent realistic urban entities. This study presents a new land parcel cellular automaton (LP-CA) model for simulating urban land changes. The innovation of this model is the use of ensemble learning method for automatic calibration. The proposed model is applied in Shenzhen, China. The experimental results indicate that bagging-Naïve Bayes yields the highest calibration accuracy among a set of selected classifiers. The assessment of neighborhood sensitivity suggests that the LP-CA model achieves the highest simulation accuracy with neighbor radius r = 2. The calibrated LP-CA is used to project future urban land use changes in Shenzhen, and the results are found to be consistent with those specified in the official city plan.     

基于动态约束的元胞自动机与复杂城市系统的模拟

为获得复杂城市系统更理想的模拟效果,提出时空动态约束的城市元胞自动机(CA)模型。用不同区域、不同时间新增加的城市用地总量作为CA模型的约束条件,形成时空动态约束的CA模型,并利用该模型模拟1988—2010年东莞市和深圳市城市扩张过程。结果表明,利用CA模型模拟的1993年城市用地总精度比静态CA模型提高了5.86%,而且模型中的动态约束条件可以反映城市发展的时空差异性。     

A bottom‐up approach to discover transition rules of cellular automata using ant intelligence

This paper presents a new method to discover transition rules of geographical cellular automata (CA) based on a bottom‐up approach, ant colony optimization (ACO). CA are capable of simulating the evolution of complex geographical phenomena. The core of a CA model is how to define transition rules so that realistic patterns can be simulated using empirical data. Transition rules are often defined by using mathematical equations, which do not provide easily understandable explicit forms. Furthermore, it is very difficult, if not impossible, to specify equation‐based transition rules for reflecting complex geographical processes. This paper presents a method of using ant intelligence to discover explicit transition rules of urban CA to overcome these limitations. This ‘bottom‐up’ ACO approach for achieving complex task through cooperation and interaction of ants is effective for capturing complex relationships between spatial variables and urban dynamics. A discretization technique is proposed to deal with continuous spatial variables for discovering transition rules hidden in large datasets. The ACO–CA model has been used to simulate rural–urban land conversions in Guangzhou, Guangdong, China. Preliminary results suggest that this ACO–CA method can have a better performance than the decision‐tree CA method.     

基于神经网络的元胞自动机及模拟复杂土地利用系统

本文提出了基于神经网络的元胞自动机(CellularAutomata),并将其用来模拟复杂的土地利用系统及其演变。国际上已经有许多利用元胞自动机进行城市模拟的研究,但这些模型往往局限于模拟从非城市用地到城市用地的转变。模拟多种土地利用的动态系统比一般模拟城市演化要复杂得多,需要使用许多空间变量和参数,而确定模型的参数值和模型结构有很大困难。本文通过神经网络、元胞自动机和GIS相结合来进行土地利用的动态模拟,并利用多时相的遥感分类图像来训练神经网络,能十分方便地确定模型参数和模型结构,消除常规模拟方法所带来的弊端。     

A partitioned and asynchronous cellular automata model for urban growth simulation

Cellular automata (CA) models are used to analyze and simulate the global phenomenon of urban growth. However, these models are characterized by ignoring spatially heterogeneous transition rules and asynchronous evolving rates, which make it difficult to improve urban growth simulations. In this paper, a partitioned and asynchronous cellular automata (PACA) model was developed by implementing the spatial heterogeneity of both transition rules and evolving rates in urban growth simulations. After dividing the study area into several subregions by k-means and knn-cluster algorithms, a C5.0 decision tree algorithm was employed to identify the transition rules in each subregion. The evolving rates for cells in each regularly divided grid were calculated by the rate of changed cells. The proposed PACA model was implemented to simulate urban growth in Wuhan, a large city in central China. The results showed that PACA performed better than traditional CA models in both a cell-to-cell accuracy assessment and a shape dimension accuracy assessment. Figure of merit of PACA is 0.368 in this research, which is significantly higher than that of partitioned CA (0.327) and traditional CA (0.247). As for the shape dimension accuracy, PACA has a fractal dimension of 1.542, which is the closest to that of the actual land use (1.535). However, fractal dimension of traditional CA (1.548) is closer to that of the actual land use than that of partitioned CA (1.285). It indicates that partitioned transition rules play an important role in the cell-to-cell accuracy of CA models, whereas the combination of partitioned transition rules and asynchronous evolving rates results in improved cell-to-cell accuracy and shape dimension accuracy. Thus, implementing partitioned transition rules and asynchronous evolving rates yields better CA model performance in urban growth simulations due to its accordance with actual urban growth processes.     

Integrated modelling of population,employment and land-use change with a multiple activity-based variable grid cellular automaton

A constrained cellular automaton (CA) framework is used to model both land use and, at the same resolution, densities of population and economic activity. The multi-scale processes determining the location of population, economic activity and land use are captured in a variable grid CA, in which the neighbourhood of each cell includes the entire modelled area. The transition rules generating the spatial dynamics incorporate both the land use and the activities, and because they cover the entire modelled area, they represent interaction effects at all spatial scales; effectively, they are distance decay functions. In general, any particular cell hosts a number of activities (population, employment in various sectors) regardless of its land use, so in effect multiple land uses are modelled as multiple activities, although activity levels are normally highest on cells of the corresponding land use. The model is applied to both the urban-centred Greater Dublin Region and the country of Belgium, which consists of the entire polycentric urban system and its rural matrix. Results for both applications are good, as measured by the errors of both predicted populations and fractal dimensions, and the model outperforms the best existing models by these measures.     

An extended cellular automaton using case‐based reasoning for simulating urban development in a large complex region

Rule‐based cellular automata (CA) have been increasingly applied to the simulation of geographical phenomena, such as urban evolution and land‐use changes. However, these models have difficulties and uncertainties in soliciting transition rules for a large complex region. This paper presents an extended cellular automaton in which transition rules are represented by using case‐based reasoning (CBR) techniques. The common k‐NN algorithm of CBR has been modified to incorporate the location factor to reflect the spatial variation of transition rules. Multi‐temporal remote‐sensing images are used to obtain the adaptation knowledge in the temporal dimension. This model has been applied to the simulation of urban development in the Pearl River Delta which has a hierarchy of cities. Comparison indicates that this model can produce more plausible results than rule‐based CA in simulating this large complex region in 1988–2002.     

基于元胞自动机的城市发展密度模拟

元胞自动机CA越来越多地被用于模拟复杂的城市系统,但这些模拟基本不考虑城市的发展密度。不同的城市发展密度会对城市的形态有很大的影响,有必要将城市的发展密度引进CA的城市模拟中,以获得更好的模拟结果。本文将密度梯度函数引进了CA模型的转换规则中,并定义‘灰度’来反映状态的转换。利用该模型对不同可能的城市发展组合进行了模拟,为城市规划提供了辅助依据。     

Characterization of neighborhood sensitivity of an irregular cellular automata model of urban growth

The neighborhood definition, which determines the influence on a cell from its nearby cells within a localized region, plays a critical role in the performance of a cellular automaton (CA) model. Raster CA models use a cellular grid to represent geographic space, and are sensitive to the cell size and neighborhood configuration. However, the sensitivity of vector-based CAs, an alternative to the raster-based counterpart, to neighborhood type and size remains uninvestigated. The present article reports the results of a detailed sensitivity analysis of an irregular CA model of urban land use dynamics. The model uses parcel data at the cadastral scale to represent geographic space, and was implemented to simulate urban growth in Central Texas, USA. Thirty neighborhood configurations defined by types and sizes were considered in order to examine the variability in the model outcome. Results from accuracy assessments and landscape metrics confirmed the model’s sensitivity to neighborhood configurations. Furthermore, the centroid intercepted neighborhood with a buffer of 120 m produced the most accurate simulation result. This neighborhood produced scattered development while the centroid extent-wide neighborhood resulted in a clustered development predominantly near the city center.     

基于随机森林的元胞自动机城市扩展模拟——以佛山市为例

本文提出一种基于随机森林的元胞自动机城市扩展(RF-CA)模型。通过在多个决策树的生成过程中分别对训练样本集和分裂节点的候选空间变量引入随机因素,提取城市扩展元胞自动机的转换规则。该模型便于并行构建,能在运算量没有显著增加的前提下提高预测的精度,对城市扩展中存在的随机因素有较强的容忍度。RF-CA模型可进行袋外误差估计,以快速获取模型参数;也可度量空间变量重要性,解释各空间变量在城市扩展中的作用。将该模型应用于佛山市1988-2012年的城市扩展模拟中,结果表明,与常用的逻辑回归模型相比,RF-CA模型进行模拟和预测分别能够提高1.7%和2.6%的精度,非常适用于复杂非线性特征的城市系统演变模型与扩展研究;通过对影响佛山市城市扩展的空间变量进行重要性度量,发现对佛山城市扩张模拟研究而言,距国道的距离与距城市中心的距离具有最重要的作用。     

分析学习智能元胞自动机及优化的城市模拟

元胞自动机被广泛应用于城市及其他地理现象的模拟,模拟过程中的最大问题是如何确定模型的结构和参数。该文提出一种基于分析学习的智能优化元胞自动机,该模型在逻辑回归模型的基础上,基于分析学习的智能方法,寻找元胞自动机模型的最佳参数。该方法允许用户控制空间变量影响权重,进而模拟出不同的城市发展模式,可为城市规划提供重要参考。     

CA-Markov模型的空间尺度敏感性研究

以广州市花都区为研究区,研究利用CA-Markov模型进行土地利用变化模拟的空间尺度敏感性特征,结论如下:①元胞尺寸的选择会明显影响模拟结果,元胞尺寸越大,模拟结果精度越低。模型中存在元胞尺寸的阈值,当元胞尺寸超出该阈值时,模拟结果的精度急剧下降,因此对于元胞尺寸的选择必须要慎重。②邻域类型的选择也会对模拟结果产生影响。采用3×3冯诺依曼邻域的模拟结果会比3×3摩尔邻域和5×5摩尔邻域生成更多的斑块数量和更高的斑块密度,但是模拟结果的Kappa系数值相差不大。     

A high-performance cellular automata model for urban simulation based on vectorization and parallel computing technology

Cellular automata (CA) models can simulate complex urban systems through simple rules and have become important tools for studying the spatio-temporal evolution of urban land use. However, the multiple and large-volume data layers, massive geospatial processing and complicated algorithms for automatic calibration in the urban CA models require a high level of computational capability. Unfortunately, the limited performance of sequential computation on a single computing unit (i.e. a central processing unit (CPU) or a graphics processing unit (GPU)) and the high cost of parallel design and programming make it difficult to establish a high-performance urban CA model. As a result of its powerful computational ability and scalability, the vectorization paradigm is becoming increasingly important and has received wide attention with regard to this kind of computational problem. This paper presents a high-performance CA model using vectorization and parallel computing technology for the computation-intensive and data-intensive geospatial processing in urban simulation. To transfer the original algorithm to a vectorized algorithm, we define the neighborhood set of the cell space and improve the operation paradigm of neighborhood computation, transition probability calculation, and cell state transition. The experiments undertaken in this study demonstrate that the vectorized algorithm can greatly reduce the computation time, especially in the environment of a vector programming language, and it is possible to parallelize the algorithm as the data volume increases. The execution time for the simulation of 5-m resolution and 3 × 3 neighborhood decreased from 38,220.43 s to 803.36 s with the vectorized algorithm and was further shortened to 476.54 s by dividing the domain into four computing units. The experiments also indicated that the computational efficiency of the vectorized algorithm is closely related to the neighborhood size and configuration, as well as the shape of the research domain. We can conclude that the combination of vectorization and parallel computing technology can provide scalable solutions to significantly improve the applicability of urban CA.     

Using neural networks and cellular automata for modelling intra‐urban land‐use dynamics

Empirical models designed to simulate and predict urban land‐use change in real situations are generally based on the utilization of statistical techniques to compute the land‐use change probabilities. In contrast to these methods, artificial neural networks arise as an alternative to assess such probabilities by means of non‐parametric approaches. This work introduces a simulation experiment on intra‐urban land‐use change in which a supervised back‐propagation neural network has been employed in the parameterization of several biophysical and infrastructure variables considered in the simulation model. The spatial land‐use transition probabilities estimated thereof feed a cellular automaton (CA) simulation model, based on stochastic transition rules. The model has been tested in a medium‐sized town in the Midwest of São Paulo State, Piracicaba. A series of simulation outputs for the case study town in the period 1985–1999 were generated, and statistical validation tests were then conducted for the best results, based on fuzzy similarity measures.     

An improved artificial bee colony algorithm for optimal land-use allocation

Land-use allocation is of great importance for rapid urban planning and natural resource management. This article presents an improved artificial bee colony (ABC) algorithm to solve the spatial optimization problem. The new approach consists of a heuristic information-based pseudorandom initialization (HIPI) method for initial solutions and pseudorandom search strategy based on a long-chain (LC) mechanism for neighborhood searches; together, these methods substantially improve the search efficiency and quality when handling spatial data in large areas. We evaluated the approach via a series of land-use allocation experiments and compared it with particle swarm optimization (PSO) and genetic algorithm (GA) methods. The experimental results show that the new approach outperforms the current methods in both computing efficiency and optimization quality.