Calibration of cellular automata models using differential evolution to simulate present and future land use

A key issue in cellular automata (CA) modeling is the minimization of the differences between the actual and simulated patterns, which can be mathematically formulated as an objective function. We develop a new hybrid model (termed DE‐CA) by integrating differential evolution (DE) into CA to solve the objective function and retrieve the optimal CA parameters. Constrained relations among factors were applied in DE to generate different sets of CA parameters for prediction of future scenarios. The DE‐CA model was calibrated using historical spatial data to simulate 2016 land use in Kunming and predict multiple scenarios to the year 2026. Assessment of quantitative accuracy shows that DE‐CA yields 92.4% overall accuracy, where 6.8% is the correctly captured urban growth; further, the model reported only 5.0% false alarms and 2.6% misses. Regarding the simulation ability, our new CA model performs as well as the widely applied genetic algorithm‐based CA model, and outperforms both the logistic regression‐based CA model and a no‐change NULL model. We projected three possible scenarios for the year 2026 using DE‐CA to adequately address the baseline urban growth, environmental protection and urban planning to show the strong prediction ability of the new model.     

A grey wolf optimizer–cellular automata integrated model for urban growth simulation and optimization

This article proposes a grey wolf optimizer (GWO) and cellular automata (CA) integrated model for the simulation and spatial optimization of urban growth. A new grey wolf‐inspired approach is put forward to determine the urban growth rules of CA cells by using the GWO algorithm, which is suitable for solving optimization problems. The inspiration for GWO comes from the social leadership of wolf groups, as well as their hunting behavior. The GWO‐optimized urban growth rules for CA describe the relationship between the spatial variables and the urban land‐use status for each cell in the formation of “if–then.” The GWO algorithm and CA model are then integrated as the GWO–CA model for urban growth simulation and optimization. By taking Nanjing City as an example, the simulation accuracy in terms of urban cells is 86.6%, and the kappa coefficient is 0.715, indicating that the GWO algorithm is efficient at obtaining urban growth rules from spatial variables. The validation of the GWO–CA model also illustrates that it performs well in terms of the simulation and spatial optimization of urban growth, and can further contribute to urban planning and management.     

Simulating urban growth processes by integrating cellular automata model and artificial optimization in Binhai New Area of Tianjin,China

This study presents an optimized algorithm into the cellular automata (CA) models for urban growth simulation in Binhai New Area of Tianjin, China. The optimized CA model by particle swarm optimization (PSO) was compared with the logistic-based cellular automata (LOGIT-CA) model to see the effects of the simulation. The study evaluated the stochastic disturbance in the development of urban growth using the Monte Carlo method; the coefficient d determined the state of urban growth. The validation was conducted by both cross-tabulation test and structural measurements. The results showed that the simulations of PSO-CA were better than LOGIT-CA model, indicating an improvement in the spatio-temporal simulation of urban growth and land use changes in study area. Since the simulations reached their best values when the coefficient was between 1 and 2, the urban growth in the study area was in the period of conversion from spontaneous growth to edge-expansion and infilling growth.     

Integration of neural networks and cellular automata for urban planning

This paper presents a new type of cellular automata (CA) model for the simulation of alternative land development using neural networks for urban planning. CA models can be regarded as a planning tool because they can generate alternative urban growth. Alternative development patterns can be formed by using different sets of parameter values in CA simulation. A critical issue is how to define parameter values for realistic and idealized simulation. This paper demonstrates that neural networks can simplify CA models but generate more plausible results. The simulation is based on a simple three-layer network with an output neuron to generate conversion probability. No transition rules are required for the simulation. Parameter values are automatically obtained from the training of network by using satellite remote sensing data. Original training data can be assessed and modified according to planning objectives. Alternative urban patterns can be easily formulated by using the modified training data sets rather than changing the model.     

Simulating urban growth in a megalopolitan area using a patch‐based cellular automata

Although traditional cellular automata (CA)‐based models can effectively simulate urban land‐use changes, they typically ignore the spatial evolution of urban patches, due to their use of cell‐based simulation strategies. This research proposes a new patch‐based CA model to incorporate a spatial constraint based on the growth patterns of urban patches into the conventional CA model for reducing the uncertainty of the distribution of simulated new urban patches. In this model, the growth pattern of urban patches is first estimated using a developed indicator that is based on the local variations in existing urban patches. The urban growth is then simulated by integrating the estimated growth pattern and land suitability using a pattern‐calibrated method. In this method, the pattern of new urban patches is gradually calibrated toward the dominant growth pattern through the steps of the CA model. The proposed model is applied to simulate urban growth in the Tehran megalopolitan area during 2000–2006–2012. The results from this model were compared with two common models: cell‐based CA and logistic‐patch CA. The proposed model yields a degree of patch‐level agreement that is 23.4 and 7.5% higher than those of these pre‐existing models, respectively. This reveals that the patch‐based CA model simulates actual development patterns much better than the two other models.     

Exploring land use policy scenarios with the use of a cellular automata-based model: urban sprawl containment and sustainable development in Thessaloniki

This study addresses the issue of urban sprawl through the application of a cellular automata (CA)-based model in the area of Thessaloniki, Greece. The model integrates a multiple regression model at the regional level with a CA model at the local level. New urban land is allocated in a disaggregated field of land units (cells) taking into account a wide range of data. Particular emphasis is placed on the way zoning regulations and land availability data are inserted into the model, so that alternative land use policy scenarios could be examined. Thessaloniki, a typical Mediterranean city, is used as a case study. The model is used to compare two scenarios of urban growth up to year 2030; the first one assuming a continuation of existing trends, whereas the second one assuming the enactment of various land use zoning regulations in order to contain urban sprawl.     

Integration of neural networks and cellular automata for urban planning

This paper presents a new type of cellular automata (CA) model for the simulation of alternative land development using neural networks for urban planning. CA models can be regarded as a planning tool because they can generate alternative urban growth. Alternative development patterns can be formed by using different sets of parameter values in CA simulation. A critical issue is how to define parameter values for realistic and idealized simulation. This paper demonstrates that neural netowrks can simplify CA models but generate more plausible results. The simulation is based on a simple three-layer network with an output neuron to generate conversion probability. No transition rules are required for the simulation. Parameter values are automatically obtained from the training of network by using satellite remote sensing data. Original training data can be assessed and modified according to planning objectives. Alternative urban patterns can be easily formulated by using the modified training data sets rather than changing the model.     

“三规合一”服务的空间信息技术:地理模拟与优化

中国的国民经济和社会发展规划、土地利用总体规划以及城乡规划都是法定规划,但由于规划主体、技术标准和编制办法、实施手段和监督机制等的不同,导致"三规分离"、各个规划之间相互冲突的问题较为突出。虽然国家为了消除冲突,正在开展"三规合一"的有关工作,但缺乏有关技术手段的支持。本文以地理信息科学为出发点,对地理过程建模在国内外研究中的应用进行了总结,阐述了地理模拟与优化的框架体系可以成为目前中国正在进行的"三规合一"工作的重要理论和方法支撑。     

Improving urban cellular automata performance by integrating global and geographically weighted logistic regression models

In many of the conventional cellular automata (CA) models, particularly Urban‐CA which are used for urban growth, the spatial heterogeneities and local differences of the land use conversion processes are ignored. Global logistic regression (LR) is a popular model employed to define the transition rules of Urban‐CA. By considering the local characteristics, Geographically Weighted Logistic Regression (GWLR) provides interesting capabilities for urban growth modelling. In this research, in addition to using GWLR in the definition of transition rules, the advantages of integrating GWLR and LR for urban growth simulation were evaluated; these have not been considered in previous studies. Local and global probabilities obtained from the calibration of GWLR and LR were combined to define the transition rules of an Urban‐CA. Urban growth was simulated in the Islamshahr sub‐region located southwest of Tehran, Iran for the two periods 1992‐1996 and 1996‐2002, and data from these periods were used for training and testing the prediction abilities, respectively. In the first period, GWLR showed good performance and a significant contribution to the enhancement of the simulation performance, but in the second period, the effectiveness of LR on the prediction accuracy increased. Due to their complementary roles, the integration of the GWLR and LR models resulted in improved simulation performance in both periods.     

A multi‐label cellular automata model for land change simulation

The use of cellular automata (CA) has for some time been considered among the most appropriate approaches for modeling land‐use changes. Each cell in a traditional CA model has a state that evolves according to transition rules, taking into consideration its own and its neighbors’ states and characteristics. Here, we present a multi‐label CA model in which a cell may simultaneously have more than one state. The model uses a multi‐label learning method—a multi‐label support vector machine, Rank‐SVM—to define the transition rules. The model was used with a multi‐label land‐use dataset for Luxembourg, built from vector‐based land‐use data using a method presented here. The proposed multi‐label CA model showed promising performance in terms of its ability to capture and model the details and complexities of changes in land‐use patterns. Applied to historical land use data, the proposed model estimated the land use change with an accuracy of 87.2% exact matching and 98.84% when including cells with a misclassification of a single label, which is comparably better than a classical multi‐class model that achieved 83.6%. The multi‐label cellular automata outperformed a model combining CA and artificial neural networks. All model goodness‐of‐fit comparisons were quantified using various performance metrics for predictive models.     

A Patch‐based Cellular Automaton for Simulating Land‐use Changes at Fine Spatial Resolution

While cellular automata have become popular tools for modeling land‐use changes, there is a lack of studies reporting their application at very fine spatial resolutions (e.g. 5 m resolution). Traditional cell‐based CA do not generate reliable results at such resolutions because single cells might only represent components of land‐use entities (i.e. houses or parks in urban residential areas), while recently proposed entity‐based CA models usually ignore the internal heterogeneity of the entities. This article describes a patch‐based CA model designed to deal with this problem by integrating cell and object concepts. A patch is defined as a collection of adjacent cells that might have different attributes, but that represent a single land‐use entity. In this model, a transition probability map was calculated at each cell location for each land‐use transition using a weight of evidence method; then, land‐use changes were simulated by employing a patch‐based procedure based on the probability maps. This CA model, along with a traditional cell‐based model were tested in the eastern part of the Elbow River watershed in southern Alberta, Canada, an area that is under considerable pressure for land development due to its proximity to the fast growing city of Calgary. The simulation results for the two models were compared to historical data using visual comparison, K_simulation indices, and landscape metrics. The results reveal that the patch‐based CA model generates more compact and realistic land‐use patterns than the traditional cell‐based CA. The K_simulation values indicate that the land‐use maps obtained with the patch‐based CA are in higher agreement with the historical data than those created by the cell‐based model, particularly regarding the location of change. The landscape metrics reveal that the patch‐based model is able to adequately capture the land‐use dynamics as observed in the historical data, while the cell‐based CA is not able to provide a similar interpretation. The patch‐based approach proposed in this study appears to be a simple and valuable solution to take into account the internal heterogeneity of land‐use classes at fine spatial resolutions and simulate their transitions over time.     

Enhancing a GIS Cellular Automata Model of Land Use Change: Bayesian Networks, Influence Diagrams and Causality

Cellular Automata (CA) models at present do not adequately take into account the relationship and interactions between variables. However, land use change is influenced by multiple variables and their relationships. The objective of this study is to develop a novel CA model within a geographic information system (GIS) that consists of Bayesian Network (BN) and Influence Diagram (ID) sub‐models. Further, the proposed model is intended to simplify the definition of parameter values, transition rules and model structure. Multiple GIS layers provide inputs and the CA defines the transition rules by running the two sub‐models. In the BN sub‐model, land use drivers are encoded with conditional probabilities extracted from historical data to represent inter‐dependencies between the drivers. Using the ID sub‐model, the decision of changing from one land use state to another is made based on utility theory. The model was applied to simulate future land use changes in the Greater Vancouver Regional District (GVRD), Canada from 2001 to 2031. The results indicate that the model is able to detect spatio‐temporal drivers and generate various scenarios of land use change making it a useful tool for exploring complex planning scenarios.     

An Artificial-Neural-Network-based,Constrained CA Model for Simulating Urban Growth

Insufficient research has been done on integrating artificial-neural-network-based cellular automata (CA) models and constrained CA models, even though both types have been studied for several years. In this paper, a constrained CA model based on an artificial neural network (ANN) was developed to simulate and forecast urban growth. Neural networks can learn from available urban land-use geospatial data and thus deal with redundancy, inaccuracy, and noise during the CA parameter calibration. In the ANN-Urban-CA model we used, a two-layer Back-Propagation (BP) neural network has been integrated into a CA model to seek suitable parameter values that match the historical data. Each cell's probability of urban transformation is determined by the neural network during simulation. A macro-scale socio-economic model was run together with the CA model to estimate demand for urban space in each period in the future. The total number of new urban cells generated by the CA model was constrained, taking such exogenous demands as population forecasts into account. Beijing urban growth between 1980 and 2000 was simulated using this model, and long-term (2001–2015) growth was forecast based on multiple socio-economic scenarios. The ANN-Urban-CA model was found capable of simulating and forecasting the complex and non-linear spatial-temporal process of urban growth in a reasonably short time, with less subjective uncertainty.     

元胞自动机（CA）模型在土地利用领域的研究综述

通过模型对区域土地利用/覆盖变化（LUCC）进行分析已经成为了当前全球的研究主要内容之一。元胞自动机（CA）模型是一种通过定义局部的简单的计算规则来模拟和表示整个系统中复杂现象的时空动态模型,其＂自下而上＂的研究思路,强大的复杂计算功能及高度动态,使得它在模拟空间复杂系统的时空动态演变方面具有很强的能力。CA模型通过与其他模型相结合,在综合考虑各种限制因素和转换规则的前提下,通过反复迭代综合空间分析与非空间分析,模拟土地利用变化情景,在国内外已经形成了较为成熟的研究模型。本文首先提出了CA模型在土地利用变化中应用的背景及其特点;然后,分析了CA模型的构成原理以及在国内外的应用进展与现状;最后,详细阐述了CA模型在土地利用变化中的发展趋势及今后研究工作中应注意的问题。     

基于GeoSOS的城市扩展模拟——以旅顺口区为例

运用MCE-CA和Logistic-CA两种基本的元胞自动机模型作为理论模型,考虑边界到市中心、镇中心、铁路和主要公路等作为区位因素的空间距离约束条件,以及地形和禁止建设区作为区位因素的全局限制约束条件,在地理模拟优化系统(Geographical Simulation and Optimization System,GeoSOS)的支持下,对1990~2000年和2000~2010年辽宁省大连市旅顺口区的城市空间扩展进行了模拟,并取得较好效果。结果表明,MCE-CA模型的Kappa系数分别为0.71和0.64,Logistic-CA模型分别为0.54和0.55,两者均达到较好的模拟精度;MCECA模型适用于主观变量较多的CA模型,Logistic-CA模型更适合于客观因素较多的CA模型;利用合理的CA模型模拟旅顺口区城市未来土地利用变化,可为今后的土地规划以及制定有效的土地管理措施和方针政策提供依据。     

Knowledge Transfer for Large‐Scale Urban Growth Modeling Based on Formal Concept Analysis

Cellular automata (CA) are useful for studies on urban growth and land‐use changes. Although various methods have been developed to define transition rules, modeling urban growth of large areas remains a tough challenge owing to heterogeneous geographical features. To address the problem, we present a novel method based on the combination of Formal Concept Analysis (FCA) and knowledge transfer techniques. FCA is used to solicit association rules among cities within a large area. This method can provide a theoretical basis for the knowledge transfer process. A cutting‐edge algorithm called TrAdaBoost is then integrated with the commonly‐used Logistic‐CA as the modeling framework. The proposed method is applied to the urban growth modeling of Guangdong Province, a large region with 21 cities in China, from 2005 to 2008. Compared with traditional methods, this method can achieve better results at the provincial and local levels, according to the experiments. The combination of FCA and knowledge transfer is expected to provide a useful tool for calibrating large‐scale urban CA models.     

基于支持向量机的元胞自动机及土地利用变化模拟

提出了利用遥感数据，并采用支持向量机来确定元胞自动机非线性转换规则的新方法。元胞自动机在模拟复杂地理现象时，需要采用非线性转换规则。目前元胞自动机主要采用线性方法来获取转换规则，在反映复杂的非线性地理现象时有一定的局限性。以城市扩张的模拟为例，将模拟城市系统的主要特征变量映射到Hilbert空间后，通过SVM建立最优分割超平面，分割超平面的分类决策函数由径向基核（Radial Basis Kernel）构造。利用历史遥感数据校正超平面的决策函数，确定城市元胞自动机的非线性转换规则，计算出城市发展概率。利用所提出的方法，对深圳市1988-2010年的城市发展进行了模拟，取得了较理想的模拟效果。研究结果表明，基于SVM-CA模型的模拟精度比传统MCE方法模拟精度高，MoranⅠ指数与实际更为接近。     

Exploring the Historical Determinants of Urban Growth Patterns through Cellular Automata

We have adapted METRONAMICA, an established cellular automata (CA) modelling system, to simulate the historical growth of a section of a large world city. Our model is tuned to reflect the morphology of land use patterns more accurately than traditional CA models, which abstract those patterns to more aggregate spatial scales. We explore the spatial determinants of land use patterns with detailed empirical data, documenting the historical growth of West London at an unusually high level of spatial and temporal resolution. The results of the study provide support for our considered speculations: (1) that the spatial relationships between land uses and the physical environment are remarkably consistent through time, showing little variation relative to changes in historical context; and (2) that these relationships constitute a basic code for urban growth which determines the spatial signature of land development in a given metropolitan area.     

MonoLoop:CA城市模型状态转换规则获取的一种方法

状态转换规则是元胞自动机(Cellular Automata,CA)的核心,如何获取并建立CA的状态转换规则是构建CA模型的关键。邻域作用是CA能够模拟复杂物理现象的核心驱动力,而在已有的用于城市增长模拟的CA城市模型中,因为邻域作用在模拟的过程中为时间动态的变量,其系数很难通过常用的Logistic回归方法识别,致使已有的CA城市模型的状态转换规则中,往往仅通过Logistic回归获取邻域作用之外的空间变量的模型参数,而邻域作用的参数通常采用主观赋值的方法。本文提出了CA城市模型的多指标评价(Multi-Criteria Evalua-tion,MCE)形式状态转换规则获取的一种新方法 MonoLoop,并针对北京市域1976～2006年的城市增长开展了该方法的实验。基于这种方法,一方面利用历史数据可以建立更为客观的状态转换规则;另一方面也可以大大降低模型参数识别的时间。     

A novel approach for predicting the spatial patterns of urban expansion by combining the chi-squared automatic integration detection decision tree,Markov chain and cellular automata models in GIS

Urban development is a continuous and dynamic spatio-temporal phenomenon associated with economic developments and growing populations. To understand urban expansion, it is important to establish models that can simulate urbanization process and its deriving factors behaviours, monitor deriving forces interactions and predict spatio-temporally probable future urban growth patterns explicitly. In this research, therefore, we presented a hybrid model that integrates the chi-squared automatic integration detection decision tree (CHAID-DT), Markov chain (MC) and cellular automata (CA) models to analyse, simulate and predict future urban expansions in Tripoli, Libya in 2020 and 2025. First, CHAID-DT model was applied to investigate the contributions of urban factors to the expansion process, to explore their interactions and to provide future urban probability map; second, MC model was employed to estimate the future demand of urban land; third, CA model was used to allocate estimated urban land quantity on the probability map to present future projected land use map. Three satellite images of the study area were obtained from the periods of 1984, 2002 and 2010 to extract land use maps and urban expansion data. We validated the model with two methods, namely, receiver operating characteristic and the kappa statistic index of agreement. Results confirmed that the proposed hybrid model could be employed in urban expansion modelling. The applied hybrid model overcame the individual shortcomings of each model and explicitly described urban expansion dynamics, as well as the spatio-temporal patterns involved.