Cellular Automata Transition Rules Research Articles

Delineating urban growth boundaries by coupling urban interactions and ecological conservation

Urban growth boundaries (UGBs) are efficient tools for controlling disorderly urban expansion/sprawl and ensuring sustainable urban development. Previous studies have delineated UGBs from the perspective of ecological conservation or efficiency improvement and have widely applied them to spatial planning. However, few studies have investigated the role of urban interactions and connections in delineating UGBs, especially in rapidly developing urban agglomerations. Our study proposed a novel framework for UGBs delineation in urban agglomerations by coupling urban interactions and ecological conservation, with two innovative points. First, interurban interactions and connections were quantified to elucidate the transition rules of cellular automata (CA), and ecological conservation was configured as a constraint of the CA model. Second, the hierarchical generalized linear model (HGLM)-CA model was used to simulate the urban land pattern in 2035, and the dilation-erosion algorithm realized the final UGBs. The proposed framework was applied to UGBs delineation in the Changsha-Zhuzhou-Xiangtan (CZX) urban agglomeration, a rapidly developing urban agglomeration in China. Furthermore, a comparison among multi-scenario UGBs shows that urban interactions and connections can accelerate the clustering of urban development, and the delineated UGBs are more practical. Our study highlighted the importance of urban interactions for UGBs delineation in urban agglomerations and evaluated a case of UGBs delineation to validate our appeal.

A hybrid modeling approach considering spatial heterogeneity and nonlinearity to discover the transition rules of urban cellular automata models

Urban sprawl is a typical geographic dynamic process with spatial heterogeneity and nonlinearity. However, current studies usually focus on only one of them to extract urban sprawl mechanisms and build cellular automata (CA) models. In the current work, the urban CA transition rules are derived by a geographically weighted artificial neural network (GWANN), which can discover the driving mechanism of urban sprawl by considering both spatial heterogeneity and nonlinearity. Taking the urban sprawl of Wuhan and Beijing during 2000–2020 as examples, the advantages of GWANN in deriving transition rules are investigated by comparing it with logistic regression (LR), geographically weighted logistic regression (GWLR), and artificial neural network (ANN). Furthermore, the simulation performance of CA models based on LR, GWLR, ANN, and GWANN is compared and analyzed from the aspects of global and regional simulation accuracy and the morphology of simulated urban patches. The results show that GWANN has better fitting and simulation performance, indicating the validity and necessity of coupling spatial heterogeneity and nonlinearity to establish transition rules. This study is a novel exploration that contributes to deriving CA transition rules through a hybrid modeling approach that couples statistical models with learning models.

Urban growth modeling based on cellular automata with transition rules optimized using genetic fuzzy systems

AbstractThis article presents a new methodology for urban growth modeling by integrating cellular automata (CA) and genetic fuzzy algorithms. The urban growth phenomenon is a spatio‐temporal and continuous process that can be modeled by employing fuzzy logic as a framework for handling vagueness. Dependence upon an expert for assigning membership functions and rule weights has made the fuzzy logic approach rather subjective. Our proposed methodology overcomes this shortcoming by applying genetic algorithms to tune and optimize the fuzzy logic system and to make it expert independent. The optimization process encompasses a fuzzy membership function and weights for fuzzy rules. This model uses linguistic variables for defining CA transition rules and applies them to represent the non‐deterministic nature of urban growth. The proposed model is applied to simulate urban growth in the Tehran Metropolitan Area in Iran across time steps of 1988, 1999, and 2010 developed using Landsat TM and ETM+ images and a Digital Elevation Model. The first data pairs were employed for calibration of the model parameters, and the remainder of the data was used for validation of the model across time. The model was evaluated using a relative operating characteristic of 0.88 and a figure of merit statistic of 0.31, which quantifies the model goodness of fit.

Simulating mixed land-use change under multi-label concept by integrating a convolutional neural network and cellular automata: a case study of Huizhou, China

ABSTRACT Cellular automata (CA) model is a useful tool for simulating spatiotemporal changes of land-use evolution. However, previous CA models have usually ignored the inhomogeneous and mixed land-use situations and simplified the land grid cell as one single land-use type. This study developed a multi-label (ML) convolutional neural network CA (ML-CNN-CA) model to simulate the complex evolution of mixed land uses. The multi-label learning strategy in the proposed model can formulize mixed land uses by labeling multiple land-use types to each grid cell. The transition rules of CA were modified to accommodate the multi-label learning strategy and mined by coupling a CNN network and three interactive mechanisms, including the neighborhood effect, adaptive inertia coefficient, and random factor. The proposed ML-CNN-CA model was applied and examined in a fast-developing city (Huizhou) in the China’s Pearl River Delta region for the mixed land-use simulation during 2009–2013 and 2013–2020. The ML-CNN-CA model with different CNN architectures and a previous artificial neural network (ANN)-based multi-label CA model were also implemented for comparisons. Results show the capability of the ML-CNN-CA model to simulate fine-scale mixed land-use changes with satisfactory performances. Specifically, the simulated mixed land-use patterns agree well with the actual land uses from the morphological perspective. Furthermore, the quantitative assessments demonstrate the performance of the proposed model, showing an accuracy value of 0.912 for 2009–2013 and 0.896 for 2013–2020, and a hamming loss value of 0.048 for 2009–2013 and 0.055 for 2013–2020. The comparisons also show the best performance of the ML-CNN-CA model with the VGG-based architecture and significant outperformance of the proposed model against the previous ANN-based CA model. Multiple sensitivity analyses were also conducted to investigate the uncertainty of the proposed model. The ML-CNN-CA model proposed in this study can provide a new tool for better simulation of fine-scale mixed land-use changes and is expected to help formulate urban planning guidelines and achieve sustainable urban development.

Spatially-explicit prediction of low-density peri-urban development: comparison between urban and rural scenarios in the Moreton Bay Region in South East Queensland, Australia

Mainstream urban modelling literature focuses on urban expansion featured by a relatively fast urbanisation process, but relatively less research is available to understand and model the slow-paced urban and rural land development in the low-density peri-urban context. This study aims to address this knowledge gap by simulating the urban and rural land development in the Moreton Bay Region in South East Queensland (SEQ), Australia using two cellular automata (CA) models that are coupled with a generalised simulated annealing (GSA) algorithm. With the total land available for development estimated using a Markov Chain model, the GSA-CA urban and rural models were developed, respectively, to simulate urban and rural land development from 1991 to 2011, and then to predict their future development to 2041 following vigorous model calibrations. The modelling results illustrate three snapshots of the predicted spatial patterns of urban and rural development in 2021, 2031 and 2041, with moderate growth in both the urban and rural areas over time, but with urban development occurring in a more compact form than rural development. The GSA-CA modelling approach is capable of optimising the CA transition rules and has the potential to be applied to other geographical contexts to support regional planning, decision-making and scenario designation for future land development in cities that have entered the saturation phase of urbanisation.

Using spatial heterogeneity to strengthen the neighbourhood effects of urban growth simulation models

ABSTRACT The transition rules of cellular automata (CA) werestrengthened by incorporating annual growth rate (AGR) to reflect spatially heterogeneous neighbourhoods. We conducted hotspot (AGRHST) and gradient (AGRGDT) analysis of AGR to generate two spatial heterogeneity layers, then constructed three CA models: AGR-CA, AGRHST-CA and AGRGDT-CA. The modeling results showed that AGR-CA performed best in overall accuracy, AGRGDT-CA was superior to other models in terms of landscape pattern, and AGRHST-CA produced unrealistically smooth boundaries. The simulation accuracy of these models exceeds 89%, indicating that logistic regression-based simulation methods can be substantially improved by strengthening the neighbourhood effects.

Cellular Automata Modelling of Discontinuous Precipitation.

The fundamentals of discontinuous precipitation (DP) reaction modelling using a cellular automata (CA) method are presented. In the proposed CA model, cell states, internal variables, equations, and transition rules were defined to predict the manner of mass transport during DP reaction and to relate changes in the microstructure with corresponding changes in chemical composition. Furthermore, the concept of digital material representation (DMR) was introduced into the CA model, which allowed schematic images of the microstructure to be used as starting structures in the modelling of the DP reaction. The preliminary assumptions adopted in the proposed CA model for the DP reaction were verified by numerical simulations of the growth of discontinuous precipitates at a steady-state at the example of Al-22 at.% Zn alloy. The outcomes achieved from the CA simulations were presented in a different form than that most commonly used previously (single concentration profiles), namely as the 2D maps showing changes in Zn content accompanying the successive stages of growth of discontinuous precipitates. The model used for the description of the solute diffusion along of the reaction front (RF) allowed two-dimensional systems at the nano-scale to be treated within a reasonable simulation time. The obtained results indicate that the developed CA model was able to realistically simulate the DP reaction, which was confirmed by the visualisation of migrating RFs together with associated chemical composition changes in the microstructure.

Reconstructing the historical patterns of forest stand based on CA-AdaBoost-ANN model

Understanding the long-term interaction between humans and the environment requires the reconstruction of historical forest dynamics. However, the accuracy of methods to reconstruct the patterns of historical forest stands using resurvey data has not been comprehensively evaluated. Previous simulations and statistical assessments of forests have focused on reconstructing land cover or single layer, but are not congruent with the specific data typically obtained by field survey. Additionally, most reconstruction studies have not reconstructed the patterns of the forest stand or the tree species distribution. In this work, we applied cellular automata (CA), which integrated artificial neural networks (ANN), to describe tree species dynamics in response to forest changes in Heishiding Nature Reserve of Guangdong province in south China. The top 70 dominant tree species represented by importance value (IV) and actual distribution were considered. The relationship of the current and historical forest distributions was modeled using an AdaBoost-based back-propagation neural network algorithm. The area under the receiver operating characteristics curve (AUC) values for the 70 studied tree species ranged from 0.8556 to 0.9981, which suggested that the reconstructed patterns were reasonable. The simulation of the forest stands of a 50-ha plot in 2012 achieved an overall accuracy of 94.14% and a Lee Sallee index of 0.7974. The results indicated that this method can be further improved to obtain a more accurate pattern of tree species by adjusting the CA transition rules and parameters. Overall, the results demonstrate that the CA-AdaBoost-ANN model can be applied as an effective path to obtain a distribution map of historical forest types, which will be extremely useful for effective forest management.

Urban Growth Modeling and Future Scenario Projection Using Cellular Automata (CA) Models and the R Package Optimx

Cellular automata (CA) is a spatially explicit modeling tool that has been shown to be effective in simulating urban growth dynamics and in projecting future scenarios across scales. At the core of urban CA models are transition rules that define land transformation from non-urban to urban. Our objective is to compare the urban growth simulation and prediction abilities of different metaheuristics included in the R package optimx. We applied five metaheuristics in optimx to near-optimally parameterize CA transition rules and construct CA models for urban simulation. One advantage of metaheuristics is their ability to optimize complexly constrained computational problems, yielding objective parameterization with strong predictive power. From these five models, we selected conjugate gradient-based CA (CG-CA) and spectral projected gradient-based CA (SPG-CA) to simulate the 2005–2015 urban growth and to project future scenarios to 2035 with four strategies for Su-Xi-Chang Agglomeration in China. The two CA models produced about 86% overall accuracy with standard Kappa coefficient above 69%, indicating their good ability to capture urban growth dynamics. Four alternative scenarios out to the year 2035 were constructed considering the overall effect of all candidate influencing factors and the enhanced effects of county centers, road networks and population density. These scenarios can provide insight into future urban patterns resulting from today’s urban planning and infrastructure, and can inform future development strategies for sustainable cities. Our proposed metaheuristic CA models are also applicable in modeling land-use and urban growth in other rapidly developing areas.

Mining transition rules of cellular automata for simulating urban expansion by using the deep learning techniques

ABSTRACTAlong with the gradually accelerated urbanization process, simulating and predicting the future pattern of the city is of great importance to the prediction and prevention of some environmental, economic and urban issues. Previous studies have generally integrated traditional machine learning with cellular automaton (CA) models to simulate urban development. Nevertheless, difficulties still exist in the process of obtaining more accurate results with CA models; such difficulties are mainly due to the insufficient consideration of neighborhood effects during urban transition rule mining. In this paper, we used an effective deep learning method, named convolution neural network for united mining (UMCNN), to solve the problem. UMCNN has substantial potential to get neighborhood information from its receptive field. Thus, a novel CA model coupled with UMCNN and Markov chain was designed to improve the performance of simulating urban expansion processes. Choosing the Pearl River Delta of China as the study area, we excavate the driving factors and the transformational relations revealed by the urban land-use patterns in 2000, 2005 and 2010 and further simulate the urban expansion status in 2020 and 2030. Additionally, three traditional machine-learning-based CA models (LR, ANN and RFA) are built to attest the practicality of the proposed model. In the comparison, the proposed method reaches the highest simulation accuracy and landscape index similarity. The predicted urban expansion results reveal that the economy will continue to be the primary factor in the study area from 2010 to 2030. The proposed model can serve as guidance in urban planning and government decision-making.

Comparison of metaheuristic cellular automata models: A case study of dynamic land use simulation in the Yangtze River Delta

Cellular automata (CA) is a bottom-up modeling framework that has increasingly been applied to simulate land use change by capturing its dynamics. Metaheuristics such as particle swarm optimization (PSO), generalized simulated annealing (GSA) and genetic algorithm (GA) have widely been incorporated into CA modeling to generate more realistic simulation patterns. We present a comparative study of four CA models incorporating logistic regression (LR) and the three metaheuristics respectively to simulate land use change in the Yangtze River Delta from 2005 to 2015. The metaheuristic processes are guided by an objective function that represents the root-mean-square error (RMSE) of the transition rules, which can then automatically search for suboptimal CA coefficients. The three metaheuristics are substantially different in terms of the algorithm mechanism, optimization iteration, and computational time. The land conversion potentials from the metaheuristics are similar in global patterns but marginally different in local regions, which substantially differ from that calculated using LR. All three metaheuristic CA models simulated slightly less than the reference change while the LR-CA model simulated substantially more than the reference change, however all models allocated the change to similar places. Our study shows that the three metaheuristics can achieve similar outcomes in the optimization of CA transition rules and land use simulation, albeit with different sensitivities to their intrinsic control parameters. We suggest that any of the three metaheuristics could be used to construct land use CA models, if the algorithm complexity and computational time are not highly concerned.

Calibrating nonparametric cellular automata with a generalized additive model to simulate dynamic urban growth

Understanding factors that drive urban growth is essential to cellular automata (CA) based urban modeling. Multicollinearity among correlated factors may cause negative effects when building CA transition rules, leading to a decrease in simulation accuracy. We use a nonparametric generalized additive model (GAM) to evaluate these relationships through flexible smooth functions to capture the dynamics of urban growth. A GAM-based CA (termed GAM-CA) model was then developed to simulate the rapid urban growth in Shanghai, China from 2000 to 2015. GAM highlights the significance of each candidate factor driving urban growth during the past 15 years. Compared to logistic regression, the GAM-CA transition rules fitted the observed data better and yielded improved overall accuracy and hence more realistic urban growth patterns. The new CA model has great potential for capturing key driving factors to simulate dynamic urban growth, and can predict future scenarios under various spatial constraints and conditions.

A new temporal–spatial dynamics method of simulating land-use change

The integration of a system dynamics (SD) model, a cellular automata (CA) model, and a Geographic Information System (GIS) is an important topic in the temporal and spatial simulation of land-use changes. Based on many previous studies, the temporal–spatial dynamics method (TSDM) has been proposed as a research framework that removes the limitations of using loosely coupled SD–CA–GIS. In this study, TSDM was successfully implemented in the NetLogo platform. The results show that: (1) Integration SD–CA–GIS based on grids leads to the seamless implementation of real-time data exchange among SD, CA, and GIS; (2) The temporal–spatial dynamic mechanisms can be represented using common time steps in SD–CA–GIS, and TSDM can be used for spatial visualization; and (3) The model accuracy can be improved by extending the CA transition rules with SD. The land-use patterns for 2000, 2010, and 2016 in Beijing, China, were simulated to test the TSDM implementation, and the simulation accuracies were 83.75%, 80.98%, and 77.40%, respectively. The results indicate that TSDM achieves a much better accuracy than conventional SD–CA–GIS coupled models, and is a more practical approach to simulate land-use change.

Integrating the multi-label land-use concept and cellular automata with the artificial neural network-based Land Transformation Model: an integrated ML-CA-LTM modeling framework

Cellular automata (CA) and artificial neural networks (ANNs) have been used by researchers over the last three decades to simulate land-use change (LUC). While conventional CA and ANN models assign a cell to only one land-use class, in reality, a cell may belong to several land-use classes simultaneously. The recently developed multi-label (ML) concept overcomes this limitation in land change science. Although the ML concept is a new paradigm with nonexclusive classes and has shown considerable merit in several applications, few studies in land change science have applied it. In addition, determining transition rules in conventional CA is difficult when the number of drivers is large. Since CA has been shown as a potential model to consider neighborhood effects and ANN has been shown effective in determining CA transition rules, we integrated both CA with an ANN model to overcome limitations of each tool. In this study, we specifically extended the ANN-based Land Transformation Model (LTM) with both a CA-based model and the ML concept to create an integrated ML-CA-LTM modeling framework. We also compared, using standard evaluation measures, differences between the proposed integrated model with a conventional CA-based LTM model (called the ml-CA-LTM). Parameterization was made using a learning and testing procedure common in machine learning. Results showed that the modified LUC model, ML-CA-LTM, produced consistently better goodness of fit calibration values compared to the ml-CA-LTM. The outcome of this modified model can be used by managers and decision makers for improved urban planning.

Discovery of Transition Rules for Cellular Automata Using Artificial Bee Colony and Particle Swarm Optimization Algorithms in Urban Growth Modeling

This paper presents an advanced method in urban growth modeling to discover transition rules of cellular automata (CA) using the artificial bee colony (ABC) optimization algorithm. Also, comparisons between the simulation results of CA models optimized by the ABC algorithm and the particle swarm optimization algorithms (PSO) as intelligent approaches were performed to evaluate the potential of the proposed methods. According to previous studies, swarm intelligence algorithms for solving optimization problems such as discovering transition rules of CA in land use change/urban growth modeling can produce reasonable results. Modeling of urban growth as a dynamic process is not straightforward because of the existence of nonlinearity and heterogeneity among effective involved variables which can cause a number of challenges for traditional CA. ABC algorithm, the new powerful swarm based optimization algorithms, can be used to capture optimized transition rules of CA. This paper has proposed a methodology based on remote sensing data for modeling urban growth with CA calibrated by the ABC algorithm. The performance of ABC-CA, PSO-CA, and CA-logistic models in land use change detection is tested for the city of Urmia, Iran, between 2004 and 2014. Validations of the models based on statistical measures such as overall accuracy, figure of merit, and total operating characteristic were made. We showed that the overall accuracy of the ABC-CA model was 89%, which was 1.5% and 6.2% higher than those of the PSO-CA and CA-logistic model, respectively. Moreover, the allocation disagreement (simulation error) of the simulation results for the ABC-CA, PSO-CA, and CA-logistic models are 11%, 12.5%, and 17.2%, respectively. Finally, for all evaluation indices including running time, convergence capability, flexibility, statistical measurements, and the produced spatial patterns, the ABC-CA model performance showed relative improvement and therefore its superiority was confirmed.

Cellular Automata for Urban Growth Modelling:

Urban growth modelling has attracted considerable attention over the past two decades. This article reviews the driving factors that have been identified and studied in cellular automata (CA); one of the popular methods in urban growth modelling. Over a hundred articles published between 1993 and 2012 were selected and reviewed. We extracted the driving factors from CA transition rules and arranged them in a list. The list contributes to early spatial research for the selection of factors in CA models. Our analyses show that studies between 1993 and 2000 mainly focused on using earth’s physical factors in predicting urban growths, while recent studies combined them with socioeconomic factors, resulting with models with a greater number of inputs. Nevertheless, the human-behaviour factors impacting urban growth were generally under-represented. Geographically, more applications of the CA urban growth models have been seen in the developed countries compared with those in the developing countries, suggesting substantial work is needed to address issues in understanding and modelling rapid urban growth processes in developing countries.

Spatial and temporal dimensions of land use change in cross border region of Luxembourg. Development of a hybrid approach integrating GIS, cellular automata and decision learning tree models

This paper presents a geographical and computational modelling approach to explore the nonlinear relationship between land use types and geospatial driving factors. It focuses on the dynamism of land use characteristics in a cross-border region. The developed model is based on fully integrated Cellular Automata (CA), Geographic Information System (GIS) and Decision Learning Tree (DLT) model, which is used to define the CA transition rules. Existing literature considers CA as one of the most relevant tools for modelling spatial changes over time, particularly when complex systems such as land use are involved. The literature also highlights that, when CA is combined with other tools, results lead to a better spatial prospect of land use dynamics. Our results reveal how land use is structured around both the transportation system and the border, and how measuring accessibility from different angles using GIS platform permits analysis of the temporal and spatial discontinuity of land use itself, thereby identifying the discontinuity components of land use patterns determined by land use boundaries.

RunCA: A cellular automata model for simulating surface runoff at different scales

Summary The Runoff Model Based on Cellular Automata (RunCA) has been developed to simulate surface runoff at different scales by integrating basic cellular automata (CA) rules with fundamental measureable hydraulic properties. In this model, a two-dimensional lattice composed of a series of rectangular cells was employed to cover the study area. Runoff production within each cell was simulated by determining the cell state (height) that consists of both cell elevation and water depth. The distribution of water flow among cells was determined by applying CA transition rules based on the minimization-of-difference algorithm and the calculated spatially varied flow velocities. RunCA was verified and validated by three steps. Good agreement with the analytical solution was achieved under simplified conditions in the first step. Then, results from runoff experiments on small laboratory plots (2 m × 1 m) showed that the model was able to well predict the hydrographs, with the mean Nash–Sutcliffe efficiency greater than 0.90. RunCA was also applied to a large scale site (Pine Glen Basin, USA) with data taken from literature. The predicted hydrograph agreed well with the measured results. Simulated flow maps in this basin also demonstrated the model capability in capturing both the spatial and temporal variations in the runoff process. Model sensitivity analysis results showed that the calculated total runoff and total infiltration were most sensitive to the input parameters representing the final steady infiltration rate at both scales. The Manning’s roughness coefficient and the setting of cell size did not affect the results much at the small plot scale, but had large influences at the large basin scale.

Modeling urban growth with GIS based cellular automata and least squares SVM rules: a case study in Qingpu–Songjiang area of Shanghai, China

A critical issue in urban cellular automata (CA) modeling concerns the identification of transition rules that generate realistic urban land use patterns. Recent studies have demonstrated that linear methods cannot sufficiently delineate the extraordinary complex boundaries between urban and non-urban areas and as most urban CA models simulate transitions across these boundaries, there is an urgent need for good methods to facilitate such delineations. This paper presents a machine learning CA model (termed MachCA) with nonlinear transition rules based on least squares support vector machines (LS-SVM) to simulate such urban growth. By projecting the input dataset into a high dimensional space using the LS-SVM method, an optimal hyper-plane is constructed to separate the complex boundaries between urban and nonurban land, thus enabling the retrieval of nonlinear CA transition rules. In the MachCA model, the transition rules are yes–no decisions on whether a cell changes its state or not, the rules being dynamically updated for each iteration of the model implementation. The application of the MachCA for simulating urban growth in the Shanghai Qingpu–Songjiang area in China reveals that the spatial configurations of rural–urban patterns can be modeled. A comparison of the MachCA model with a conventional CA model fitted by logarithmic regression (termed LogCA) shows that the MachCA model produces more hits and less misses and false alarms due to its capability for capturing the spatial complexity of urban dynamics. This results in improved simulation accuracies, although with only less than 1 % deviation between the overall errors produced by the MachCA and LogCA models. Nevertheless, the way MachCA model use in retrieving the transition rules provides a new method for simulating the dynamic process of urban growth.

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.