A new discovery of transition rules for cellular automata by using cuckoo search algorithm

This paper presents an intelligent approach to discover transition rules for cellular automata (CA) by using cuckoo search (CS) algorithm. CS algorithm is a novel evolutionary search algorithm for solving optimization problems by simulating breeding behavior of parasitic cuckoos. Each cuckoo searches the best upper and lower thresholds for each attribute as a zone. When the zones of all attributes are connected by the operator ‘And’ and linked with a cell status value, one CS-based transition rule is formed by using the explicit expression of ‘if-then’. With two distinct advantages of efficient random walk of Lévy flights and balanced mixing, CS algorithm performs well in both local search and guaranteed global convergence. Furthermore, the CA model with transition rules derived by CS algorithm (CS-CA) has been applied to simulate the urban expansion of Nanjing City, China. The simulation produces encouraging results, in terms of numeric accuracy and spatial distribution, in agreement with the actual patterns. Preliminary results suggest that this CS approach is well suitable for discovering reliable transition rules. The model validation and comparison show that the CS-CA model gets a higher accuracy than NULL, BCO-CA, PSO-CA, and ACO-CA models. Simulation results demonstrate the feasibility and practicability of applying CS algorithm to discover transition rules of CA for simulating geographical systems.     

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.     

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.     

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.     

Data mining of cellular automata's transition rules

This paper presents a new method to discover knowledge for geographical cellular automata (CA) by using a data-mining technique. CA have the ability to simulate complex geographical phenomena. Very few studies have been carried out on how to determine and validate the transition rules of CA from observed data. The transition rules of traditional CA are usually expressed by mathematical equations. This paper demonstrates that the explicit transition rules of CA can be automatically reconstructed through the rule induction procedure of data mining. The explicit transition rules are more intuitive to decision-makers. The transition rules are obtained by applying data-mining techniques to spatial data. The proposed method can reduce the uncertainties in defining transition rules and help to generate more reliable simulation results.     

基于蜂群算法的城市土地利用变化建模

通过引入人工蜂群算法用于构建土地利用变化的驱动力模型,分析土地利用变化的驱动力机制。算法原理通过模仿蜜蜂采蜜行为,自动搜索和提取土地利用变化样本中不同土地变化类型所对应的驱动力分类规则。分类规则的构建采用“IF…THEN”形式,并选取3种不同的适应度函数分别进行模拟验证。研究案例基于UCI实验数据集和美国纽卡斯尔市真实土地利用变化数据集。由实验结果可知,采用蜂群算法模型的总体精度和Kappa系数评价优于其它算法,表明蜂群算法应用于土地利用变化建模具有可行性。     

Simulating urban growth by integrating landscape expansion index (LEI) and cellular automata

Traditional urban cellular automata (CA) model can effectively simulate infilling and edge-expansion growth patterns. However, most of these models are incapable of simulating the outlying growth. This paper proposed a novel model called LEI-CA which incorporates landscape expansion index (LEI) with CA to simulate urban growth. Urban growth type is identified by calculating the LEI index of each cell. Case-based reasoning technique is used to discover different transition rules for the adjacent growth type and the outlying growth type, respectively. We applied the LEI-CA model to the simulation of urban growth in Dongguan in southern China. The comparison between logistic-based CA and LEI-CA indicates that the latter can yield a better performance. The LEI-CA model can improve urban simulation accuracy over logistic-based CA by 13.8%, 10.8% and 6.9% in 1993, 1999 and 2005, respectively. Moreover, the outlying growth type hardly exists in the simulation by logistic-based CA, while the proposed LEI-CA model performs well in simulating different urban growth patterns. Our experiments illustrate that the LEI-CA model not only overcomes the deficiencies of traditional CA but might also better understand urban evolution process.     

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.     

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.     

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。     

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.     

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。     

基于案例推理的元胞自动机及大区域城市演变模拟

元胞自动机(CA) 被越来越多地用于复杂系统的模拟中。许多地理现象的演变与其影响要素之间存在着复杂的关系, 并往往具有时空动态性。在研究区域较大和模拟时间较长时, 定义具体的规则来反映这种复杂关系有较大的困难。为了解决CA 转换规则获取的瓶颈问题, 提出了基于案例推理(CBR) 的CA 模型, 并对CBR 的k 近邻算法进行了改进, 使其能反映转换规则的时空动态性。将该模型应用于大区域的珠江三角洲城市演变中。实验结果显示, 其模拟的空间格局与实际情况吻合较好。与常规的基于Logistic 的CA 模型进行了对比, 所获得的模拟结果有更高的精度和更接近实际的空间格局, 特别在模拟较为复杂的区域时有更好的模拟效果。     

从高维特征空间中获取元胞自动机的非线性转换规则

元胞自动机 (CA) 具有强大的空间模拟能力,能够模拟和预测复杂的地理现象演变过程。CA 的核心是如何定义转换规则,但目前CA转换规则获取往往是基于线性方法来进行,例如采用多准则判断 (MCE) 技术。这些方法较难反映地理现象所涉及的非线性等复杂特征。为此提出了利用新近发展的核学习机来获取地理元胞自动机非线性转换规则的新方法。该方法是通过核函数产生隐含的高维特征空间,把复杂的非线性问题转化成简单的线性问题,为解决复杂非线性问题提供了一种非常有效的途径。利用所提出的方法自动获取地理元胞自动机的转换规则,不仅大大减少了建模所需的时间,也较好地反映地理现象复杂的特性,从而改善了CA模拟的效果。     

Modeling urban expansion by using variable weights logistic cellular automata: a case study of Nanjing,China

Simulation models based on cellular automata (CA) are widely used for understanding and simulating complex urban expansion process. Among these models, logistic CA (LCA) is commonly adopted. However, the performance of LCA models is often limited because the fixed coefficients obtained from binary logistic regression do not reflect the spatiotemporal heterogeneity of transition rules. Therefore, we propose a variable weights LCA (VW-LCA) model with dynamic transition rules. The regression coefficients in this VW-LCA model are based on VW by incorporating a genetic algorithm in a conventional LCA. The VW-LCA model and the conventional LCA model were both used to simulate urban expansion in Nanjing, China. The models were calibrated with data for the period 2000–2007 and validated for the period 2007–2013. The results showed that the VW-LCA model performed better than the LCA model in terms of both visual inspection and key indicators. For example, kappa, accuracy of urban land and figure of merit for the simulation results of 2013 increased by 3.26%, 2.96% and 4.44%, respectively. The VW-LCA model performs relatively better compared with other improved LCA models that are suggested in literature.     

Modeling urban growth in a metropolitan area based on bidirectional flows,an improved gravitational field model,and partitioned cellular automata

Simulating urban landscape dynamics in metropolitan areas has attracted much attention lately, but the difficulty remains. Although large-scale urban simulation studies consider spatial interaction as an important factor, spatial interaction cannot be accurately measured based on a single element flow, and its effects may not strictly follow a distance decay function. Furthermore, different cities may require different transition rules. In this study, we combined bidirectional flows of population and information and an improved gravitational field model to model the urban spatial interaction, and we then integrated a partitioned cellular automata (CA) model to simulate the urban growth for different cities in the Yangtze River middle reaches megalopolis. It was found that the simulation results generated by the CA model considering spatial interaction are significantly improved. Furthermore, partitioned conversion thresholds can effectively improve the model performance. The proposed model showed a much better performance in the simulation of subordinate cities surrounding the core cities, than for the core cities and fringe cities. We suggest that large-scale urban simulation should pay more attention to the development of partitioned transition rules. The effects of intercity urban flows should also be considered in the simulation of small- and medium-sized cities near the regional cores.     

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).     

A heuristic cellular automata approach for modelling urban land-use change based on simulated annealing

This article presents a novel cellular automata (CA) approach to simulate the spatio-temporal process of urban land-use change based on the simulated annealing (SA) algorithm. The SA algorithm enables dynamic optimisation of the CA's transition rules that would otherwise be difficult to configure using conventional mathematical methods. In this heuristic approach, an objective function is constructed based on a theoretical accumulative disagreement between the simulated land-use pattern and the actual land-use pattern derived from remotely sensed imagery. The function value that measures the mismatch between the actual and the simulated land-use patterns would be minimised randomly through the SA process. Hence, a set of attribution parameters that can be used in the CA model is achieved. An SA optimisation tool was developed using Matlab and incorporated into the cellular simulation in GIS to form an integrated SACA model. An application of the SACA model to simulate the spatio-temporal process of land-use change in Jinshan District of Shanghai Municipality, PR China, from 1992 to 2008 shows that this modelling approach is efficient and robust and can be used to reconstruct historical urban land-use patterns to assist with urban planning policy-making and actions. Comparison of the SACA model with a typical CA model based on a logistic regression method without the SA optimisation (also known as LogCA) shows that the SACA model generates better simulation results than the LogCA model, and the improvement of the SACA over the LogCA model is largely attributed to higher locational accuracy, a feature desirable in most spatially explicit simulations of geographical processes.     

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。