A neighbor decay cellular automata approach for simulating urban expansion based on particle swarm intelligence

Simulation and quantitative analysis of urban land use change are effective ways to investigate urban form evolution. Cellular Automata (CA) has been used as a convenient and useful tool for simulating urban land use change. However, the key issue for CA models is the definition of the transition rules, and a number of statistical or artificial intelligence methods may be used to obtain the optimal rules. Neighborhood configuration is a basic component of transition rules, and is characterized by a distance decay effect. However, many CA models do not consider the neighbor decay effect in cellular space. This paper presents a neighbor decay cellular automata model based on particle swarm optimization (PSO-NDCA). We used particle swarm optimization (PSO) to find transition rules and considered the decay effect of the cellular neighborhood. A negative power exponential function was used to compute the decay coefficient of the cellular neighborhood in the model. By calculating the cumulative differences between simulation results and the sample data, the PSO automatically searched for the optimal combination of parameters of the transition rules. Using Xiamen City as a case study, we simulated urban land use changes for the periods 1992–1997 and 2002–2007. Results showed that the PSO-NDCA model had a higher prediction accuracy for built-up land, and a higher overall accuracy and Kappa coefficient than the urban CA model based on particle swarm optimization. The study demonstrates that there exist optimal neighborhood decay coefficients in accordance with the regional characteristics of an area. Urban CA modelling should take into account the role of neighborhood decay.     

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.     

多层次矢量元胞自动机建模及土地利用变化模拟

城市规划对土地利用变化起着重要的引导作用,各层次规划相互支撑、互为补充,自上而下影响着土地利用格局的演变。矢量元胞自动机以不规则的地理实体作为基本单元,可以更逼真地表达客观复杂的城市用地空间结构。然而,当面向具有层次协同性、空间引导性和管控传导性等特征的城市规划时,其元胞多层次体系构造、层次间协同方法和转换规则获取等关键问题凸显出来。本文以江阴市2007年、2012年、2017年3期土地利用现状数据为基础,在多层次矢量元胞自动机建模基础上,模拟了2017年土地利用变化,通过模拟结果与用地现状对比分析,对模型个别参数进行了修正,进一步提高了模型的可行性与适用性,进而预测了2022年城市土地利用格局。模拟结果显示,中心城片区建设用地发展已经趋于饱和,澄南、澄东南和澄东片区建设用地扩张较为明显,有逐步形成“中心城区—城镇组团—村庄”三级城乡空间聚落体系的趋势。最后利用FoM指标对模拟结果进行了评价,得到整体和各片区的精度基本都大于或接近于0.21,表明模拟结果精度较高,其构建的模型在面向多层次规划的用地变化模拟方面具有更好的效果。     

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。     

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.     

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。     

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 systematic sensitivity analysis of constrained cellular automata model for urban growth simulation based on different transition rules

Cellular automata (CA) have emerged as a primary tool for urban growth modeling due to its simplicity, transparency, and ease of implementation. Sensitivity analysis is an important component in CA modeling for a better understanding of errors or uncertainties and their propagation. Most studies on sensitivity analyses in urban CA modeling focus on specific component such as neighborhood configuration or stochastic perturbation. However, sensitivity analysis of transition rules, which is one of the core components in CA models, has not been systematically done. This article proposes a systematic sensitivity analysis of major operational components in urban CA modeling using a stepwise comparison approach. After obtaining transition rules, three stages (i.e. static calibration of transition rules, dynamic evolution with varied time steps, and incorporation with stochastic perturbation) are designed to facilitate a comprehensive analysis. This scheme implemented with a case study in Guangzhou City (China) reveals that gaps in performance from static calibration with different transition rules can be reduced when dynamic evolution is considered. Moreover, the degree of stochastic perturbation is closely related to obtain urban morphology. However, a more realistic (i.e. fragmented) urban landscape is achieved at the cost of decreasing pixel-based accuracy in this study. Thus, a trade-off between pixel-based and pattern-based comparisons should be balanced in practical urban modeling. Finally, experimental results illustrate that models for transition rules extraction with good quality can do an assistance for urban modeling through reducing errors and uncertainty range. Additionally, ensemble methods can feasibly improve the performance of CA models when coupled with nonparametric models (i.e. classification and regression tree).     

基于约束性CA的大都市郊区城镇增长的情景模拟与管控——以武汉市江夏区为例

大都市郊区是快速城镇化进程中空间演变最为频繁、人地矛盾最为突出的区域,尤其在中国加快推进“就地就近”城镇化战略的背景下,把握大都市郊区小城镇土地利用时空变化过程及其演变机制,对制定科学合理的管控政策和优化都市空间结构具有重要的现实意义。约束性元胞自动机(constrained Cellular Automata, constrained CA)能够通过简单的规则模拟复杂的城市动态演化过程。本文将土地利用总体规划指标、城镇空间发展战略布局、土地利用开发适宜性等,嵌入约束性CA的转换规则中,采用Logistic逐步回归法分析土地利用空间影响因素,对严格约束下的武汉市江夏区2020年土地利用进行情景模拟分析,并提出城市增长管控手段。结果表明：①研究时段内,江夏区城镇用地呈低效外延式扩张,土地利用集约节约程度较低,其人口规模并未有较大增长,对主城区人口的分散作用尚未真正形成;②约束性CA在模拟大都市郊区演化方面具有较高的可靠性,能够真实反映近郊小城镇的未来空间布局与结构,模拟结果与土地利用规划和城市规划较为契合;③将规划目标导向与现实发展趋势下的模拟结果进行叠加分析,可确定城镇增长需求与规划指标调控间冲突的空间分布,从而划定土地督察的重点监测区域,为加强大都市近郊区的违法用地监查和土地利用管控提供先验的预警知识。     

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。     

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.     

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.     

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.     

基于核主成分元胞模型的城市演化重建与预测

通过元胞自动机(CA)模拟和重建城市演化的复杂非线性过程,对于城市土地利用规划和决策具有指导意义。利用传统线性方法获取的地理CA转换规则,较难刻画城市演化的时空动力学过程。基于核主成分分析方法(KPCA),通过核函数映射,在高维特征空间下不仅能够对多重共线的空间变量进行非线性降维,且由此建立的地理元胞模型KPCA-CA参数物理意义明确,能够较好地体现城市化过程的非线性本质。基于GIS环境下自主研发的地理模拟框架SimUrban,利用该KPCA-CA模型模拟和重建了快速城市化区域上海市嘉定区1989-2006年城市演化过程,并预测了研究区2010年的城市空间格局。模拟结果显示,嘉定区城市主要沿中心区域及主干道路而扩展,体现了KPCA方法提取的前两个主成分的作用,与城市实际发展情况相符。利用混淆矩阵和面积控制精度等指标,对模拟结果进行了评价,得到总体精度为80.67%、Kappa系数为61.02%,表明模拟结果与遥感分类结果及统计结果符合程度较好;与传统基于线性方法的地理CA模型比较,KPCA-CA模型模拟结果精度更高。     

Simulating land-use dynamics under planning policies by integrating artificial immune systems with cellular automata

Cellular automata (CA) have been increasingly used in simulating urban expansion and land-use dynamics. However, most urban CA models rely on empirical data for deriving transition rules, assuming that the historical trend will continue into the future. Such inertia CA models do not take into account possible external interventions, particularly planning policies, and thus have rarely been used in urban and land-use planning. This paper proposes to use artificial immune systems (AIS) as a technique for incorporating external interventions and generating alternatives in urban simulation. Inspired by biological immune systems, the primary process of AIS is the evolution of a set of ‘antibodies’ that are capable of learning through interactions with a set of sample ‘antigens’. These ‘antibodies’ finally get ‘matured’ and can be used to identify/classify other ‘antigens’. An AIS-based CA model incorporates planning policies by altering the evolution mechanism of the ‘antibodies’. Such a model is capable of generating different scenarios of urban development under different land-use policies, with which the planners will be able to answer ‘what if’ questions and to evaluate different options. We applied an AIS-based CA model to the simulation of urban agglomeration development in the Pearl River Delta in southern China. Our experiments demonstrate that the proposed model can be very useful in exploring various planning scenarios of urban development.     

基于矢量网格的城市土地利用邻里模式研究

城市土地利用的空间分布特征一直是城市地理和城市规划领域关注的重点问题,对城市土地利用空间模式的研究有助于理解城市系统的运行状态。在分析现有城市空间结构和城市土地利用模式的基础上,从两个方面对现有基于富集因子的分析方法提出改进,一是采用矢量网格以减少分析的误差,二是采用斜网格和曼哈顿距离来对空间临近关系进行界定。采用这一方法对深圳市2015年6类城市土地利用数据进行分析,得到邻里尺度上各类用地之间富集度随距离变化的3种模式。模式I中,同类用地间的富集度在短距离内较大,且其值随着距离的增加而减小并趋于0,表明同类用地间在较短距离内相互吸引,而吸引力随着距离增加而减弱。在不同类型用地间的模式II和模式III中,富集度在较短距离内为负值,但是在模式II中,富集度随着距离的增加而逐渐增加并趋于0,表明不同用地间短距离内相互排斥,且排斥作用随着距离增加而减弱;而在模式III中,富集度则随着距离增加而快速上升到正值,然后逐渐下降并趋于0,表明不同类型用地在较短距离内相互排斥,但随着距离增加很快变为相互吸引,最后吸引力随着距离增加慢慢减弱。结果表明,相对于基于栅格网的分析方法,基于矢量斜网格的分析方法能够显著降低分析误差。     

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.     

Simulating urban land use change by integrating a convolutional neural network with vector-based cellular automata

ABSTRACT

Vector-based cellular automata (VCA) models have been applied in land use change simulations at fine scales. However, the neighborhood effects of the driving factors are rarely considered in the exploration of the transition suitability of cells, leading to lower simulation accuracy. This study proposes a convolutional neural network (CNN)-VCA model that adopts the CNN to extract the high-level features of the driving factors within a neighborhood of an irregularly shaped cell and discover the relationships between multiple land use changes and driving factors at the neighborhood level. The proposed model was applied to simulate urban land use changes in Shenzhen, China. Compared with several VCA models using other machine learning methods, the proposed CNN-VCA model obtained the highest simulation accuracy (figure-of-merit = 0.361). The results indicated that the CNN-VCA model can effectively uncover the neighborhood effects of multiple driving factors on the developmental potential of land parcels and obtain more details on the morphological characteristics of land parcels. Moreover, the land use patterns of 2020 and 2025 under an ecological control strategy were simulated to provide decision support for urban planning.