Cellular Automata Transition Rules Research Articles

Calibrating a cellular automata model for understanding rural–urban land conversion: a Pareto front-based multi-objective optimization approach

Cellular automata (CA) modeling is useful to assist in understanding rural–urban land conversion processes. Although CA calibration is essential to ensuring an accurate modeling outcome, it remains a significant challenge. This study aims to address that challenge by developing and evaluating a multi-objective optimization model that considers the objectives of minimizing minus maximum likelihood estimation (MLE) value and minimizing number of errors (NOE) when calibrating CA transition rules. A Pareto front-based heuristic search algorithm, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is used to obtain optimal or near-optimal solutions. The proposed calibration approach is validated using a case study from New Castle County, Delaware, United States. A comparison of the NSGA-II-based calibration model, the generic Logit regression calibration approach (MLE-based Generic Genetic Algorithm (GGA) calibration approach), and the NOE-based GGA calibration approach demonstrates that the proposed calibration model can produce stable solutions with better simulation accuracy. Furthermore, it can generate a set of solutions with different preferences regarding the two objectives which can provide CA simulation with robust parameters options.

Markov CA, Multi Regression, and Multiple Decision Making for Modeling Historical Changes in Kirkuk City, Iraq

The cellular automata (CA) model is an important tool in land use change studies. Swift increases in population and long-term expectations of rapid urbanization have led to extensive land use change, and normal living conditions have affected the natural resources of the land. This paper highlights and analyzes the historical urban changes in Kirkuk City, Iraq, considering repeated changes undergone by the state such change as government infrastructures, wars, and economic blockade. In this paper, an integrated model, built-in multi regression model, and multi-criteria evaluation were considered to improve the representation of CA transition rules. Environmental and socioeconomic factors were used to produce Suitable Maps (SMs). These SMs were practicalities to create factor layers and weight usage, rating method process for variance expert decision-making groups, and geographic information systems for the periods 1984, 1990, 2000, and 2010. The roots of the equation (R2) values are compared and these values are chosen to produce a good model of suitable maps. The approach used in this study provides a mechanism for monitoring suitability maps in Kirkuk. Furthermore, the model Markov CA is implemented and evaluated. The results indicate that the model, its related concepts performs sufficiency

Discrete micro-scale cellular automata model for modelling phase transformation during heating of dual phase steels

Development of the discrete two-dimensional cellular automata (CA) model for modelling phase transformation during heating of dual phase (DP) steels is the subject of the present work. The model is based on the solution of fundamental diffusion equation, which is associated with local equilibrium conditions, and takes into account growth of austenite during phase transformation driven by the grain boundary curvature. Solution of the diffusion equation is realized by the finite difference method (FDM), while further growth is controlled by the cellular automata transition rules. All the details of the developed cellular automata model are presented and discussed. Finally comparison between obtained results and experimental data is also addressed.

A cellular automata model for simulating the evolution of positive–negative terrains in a small loess watershed

Cellular automata (CA) have been used increasingly to simulate complex geographical phenomena. This paper proposes a CA model for simulating the evolution of dynamic positive and negative (P–N) terrains in a small loess watershed. The CA model involves a large number of attributes, including the state of P–N terrains, distance to the shoulder-line, neighbourhood condition and topographic factors. Topographic factors include the slope gradient, aspect, slope length, slope variation, aspect variation, plan curvature, profile curvature, relief amplitude and flow accumulation. The CA model was applied to simulate the evolution of P–N terrains in an indoor, small loess watershed under artificial rainfall. The transition rules for CA were constructed automatically using a decision-tree algorithm. The derived transition rules are explicit for decision-makers and helpful for generating more reliable terrains. The simulation produces encouraging results in terms of numeric accuracy and spatial distribution, in agreement with natural P–N terrains. The iterative processes show that loess negative terrains continuously erode positive terrains. The development of a loess sinkhole near the centre gully head was reproduced as well, which shows the function of loess sinkholes in the formation of loess channel systems.

Interference of Human Impacts in Urban Growth Modelling with Transition Rules of Cellular Automata, GIS and Multi-Temporal Satellite Imagery: A Case Study of Maraghe, Iran

Urban growth is the result of physical and human impacts. In this study Cellular Automata (CA) has been used to analyze physical suitability and human forces in urban growth modelling of Maraghe. The multi-temporal satellite imagery, physical suitability and human impacts Layers have been applied to the modelling. In order to evaluate the accuracy of the image classification methods, Fuzzy ARTMAP is compared with Maximum Likelihood Classification (MLC) and Minimum Distance Classification (MDC) methods. The image classification results showed an overall accuracy of 93 %. Therefore, it is employed for classification of multi-temporal satellite imagery. In order to weight physical suitability and human impacts layers or geographical transition rules in the modelling, regression analysis, the correlation coefficient, trial-and-error method and visual comparison used. The statistical methods are presented to validate neighbourhood scales in the urban growth modelling. The calibration of the model is in fact to the estimate value of the physical suitability and human impacts layer (combinatory layer of demand for urban land and the government facilities) in the modelling. The results obtained from the model calibration showed that human impacts have the highest influence in the urban growth among other factors. Also a small neighbourhood scale (25:5 × 5 cells) is more realistic in the modeling. The accuracy of final validation is 83 % and the final scenario is based on this validation. A fuzzy CA has been used in urban growth modeling of Maraghe. The final scenario shows that Maraghe will growth on the east side, where the land demand for built up area and government facilities plays the significant role.

Synchronous cellular automata-based scheduler initialized by heuristic and modeled by a pseudo-linear neighborhood

Cellular automata (CA) are able to produce a global behavior from local interactions between their units. They have been applied to the task scheduling problem in multiprocessor systems in a very distinguished way. As this problem is NP-Complete, heuristics and meta-heuristics are usually employed. However, these techniques must always start the scheduling process from scratch for each new parallel application given as input. On the other hand, the main advantage to use CA for scheduling is the discovery of rules while solving one application and their subsequent reuse in other instances. Recently studies related to CA-based scheduling have shown relevant approaches as the use of synchronous updating in CA evolution and good results in multiprocessor systems with two processors. However, some aspects, such as the low performance of CA-based schedulers in architectures with more than two processors and during the reuse of the discovered rules, need to be investigated. This paper presents two new models to improve CA-based scheduling to deal with such aspects. The first proposal refers to the employment of a construction heuristic to initialize CA evolution and the second one is a new neighborhood model able to capture the dependence and relations strength among the tasks in a very simple way. It was named pseudo-linear neighborhood. An extensive experimental evaluation was performed using graphs of parallel programs found in the literature and new ones randomly generated. Experimental analysis showed the combined application of both techniques makes the search for CA transition rules during learning stage more robust and leads to a significant gain when considering the reuse of them on real-world conditions.

Learning from interpretation transition

We propose a novel framework for learning normal logic programs from transitions of interpretations. Given a set of pairs of interpretations (I,J) such that J=TP(I), where TP is the immediate consequence operator, we infer the program P. The learning framework can be repeatedly applied for identifying Boolean networks from basins of attraction. Two algorithms have been implemented for this learning task, and are compared using examples from the biological literature. We also show how to incorporate background knowledge and inductive biases, then apply the framework to learning transition rules of cellular automata.

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.

Modeling the spread of spatio-temporal phenomena through the incorporation of ANFIS and genetically controlled cellular automata: a case study on forest fire

Virtual representation and simulation of spatio-temporal phenomena is a promising goal for the production of an advanced digital earth. Spread modeling, which is one of the most helpful analyses in the geographic information system (GIS), plays a prominent role in meeting this objective. This study proposes a new model that considers both aspects of static and dynamic behaviors of spreadable spatio-temporal in cellular automata (CA) modeling. Therefore, artificial intelligence tools such as adaptive neuro-fuzzy inference system (ANFIS) and genetic algorithm (GA) were used in accordance with the objectives of knowledge discovery and optimization. Significant conditions in updating states are considered so traditional CA transition rules can be accompanied with the impact of fuzzy discovered knowledge and the solution of spread optimization. We focused on the estimation of forest fire growth as an important case study for decision makers. A two-dimensional cellular representation of the combustion of heterogeneous fuel types and density on non-flat terrain were successfully linked with dynamic wind and slope impact. The validation of the simulation on experimental data indicated a relatively realistic head-fire shape. Further investigations showed that the results obtained using the dynamic controlling with GA in the absence of static modeling with ANFIS were unacceptable.

Modeling land use interaction using linguistic variables

One of the main factors of land use change (LUC) modeling is the land use intersection (LUI) or neighborhood effect, which is normally modeled using cellular automata (CA) concept. The effects of LUI over distance are represented in terms of CA transition rules. In this paper, a new model for LUI process is developed that makes use of expert knowledge to define the transition rules. In this model, the region of influence is defined using a new radial structure; the transition rules are described by expert knowledge and spatial metrics in the form of linguistic variables; and finally, the neighborhood effect is classified into three groups of compactness, dependency and incompatibility. The model is implemented and evaluated using the data of Borkhar and Meymeh township, in Esfahan, Iran, for the two periods of 1986–1998 and 1998–2005. The results show that the model and its related concept are performing rather well.

Modeling dynamic urban growth using cellular automata and particle swarm optimization rules

This paper presents an improved cellular automata (CA) model of urban growth based on particle swarm optimization (PSO) approach with inertia weight. An innovative feature of this cellular model is the incorporation of swarm intelligence to stochastically optimize the transition rules to reduce the simulation uncertainties and improve its locational accuracy in urban modeling. The similarity between the nature of self-organization of particle swarm optimizers and the bottom-up approach of cellular automata makes PSO particularly suitable to search for the global optimum parameters of CA transition rules. The CA parameters retrieved by the PSO technique are able to express precisely the contributions of various driving forces to urban growth; hence an effective cellular model can be realized for modeling urban dynamics. The PSO based CA model was applied in Fengxian District of Shanghai Municipality, eastern China, to simulate the spatio-temporal process of urban growth from 1992 to 2008 at 30 m spatial resolution. The simulation outcomes, evaluated with error matrix and simulation accuracies, demonstrate that the PSO-CA model outperforms other spatial statistical based CA models.

Evolutionary Design of Cellular Automata for Noise Reduction of Grayscale Images

In this paper, we propose a new method to obtain the transition rules of two-dimensional cellular automata (CA) that performs grayscale image processing. CA has the advantages of producing complex systems from the local interaction of simple elements, and has attracted increased research interest. The difficulty of designing CA's transition rules to perform a particular task has severely limited their applications. So, the evolutionary design of CA rules has been studied. In this method, an evolutionary algorithm was used to evolve CA. In recent years, this method has been applied to image processing. Rosin has studied the evolutionary design of two-dimensional CA to perform noise reduction, thinning and convex hulls. Batouche et al. and Slatnia et al. employed genetic algorithm to investigate the possibility of CA to perform edge detection. In the previous methods, 2-state CA was used for binary image processing. Unlike the previous methods, the present method uses 256-state CA rules to perform grayscale image processing. Gene Expression Programming (GEP) proposed by Ferreira is employed as a learning algorithm in which the chromosomes encode the transition rules as expression trees. Experimental results for the reduction of impulse noise, salt-and-pepper noise and gaussian noise show that the proposed method is equivalent to previous methods in performance and more than 100 times faster than the method proposed by Rosin. We show that the rule obtained by the proposed method employs symmetry-based strategy in the noise reduction process and this property can reduce complexity of CA.

Evaluation of dynamic behavior forecasting parameters in the process of transition rule induction of unidimensional cellular automata

The simulation of the dynamics of a cellular systems based on cellular automata (CA) can be computationally expensive. This is particularly true when such simulation is part of a procedure of rule induction to find suitable transition rules for the CA. Several efforts have been described in the literature to make this problem more treatable. This work presents a study about the efficiency of dynamic behavior forecasting parameters (DBFPs) used for the induction of transition rules of CA for a specific problem: the classification by the majority rule. A total of 8 DBFPs were analyzed for the 31 best-performing rules found in the literature. Some of these DBFPs were highly correlated each other, meaning they yield the same information. Also, most rules presented values of the DBFPs very close each other. An evolutionary algorithm, based on gene expression programming, was developed for finding transition rules according a given preestablished behavior. The simulation of the dynamic behavior of the CA is not used to evaluate candidate transition rules. Instead, the average values for the DBFPs were used as reference. Experiments were done using the DBFPs separately and together. In both cases, the best induced transition rules were not acceptable solutions for the desired behavior of the CA. We conclude that, although the DBFPs represent interesting aspects of the dynamic behavior of CAs, the transition rule induction process still requires the simulation of the dynamics and cannot rely only on the DBFPs.

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.

Evolutionary Design of Rule-Changing Cellular Automata guided by Parameter indicating Propagation of Information

A method for designing the transition rules of cellular automata using genetic algorithms is described. Rule-changing cellular automata are expected to perform density classification tasks more effectively than ordinary cellular automata. We propose a method for designing high performance rule-changing cellular automata. This method uses a new parameter that indicates the propagation of information. Experimental results for density classification tasks show that the proposed method performs better than the previous method.

Cellular automata for simulating land use changes based on support vector machines

Cellular automata (CA) have been increasingly used to simulate urban sprawl and land use dynamics. A major issue in CA is defining appropriate transition rules based on training data. Linear boundaries have been widely used to define the rules. However, urban land use dynamics and many other geographical phenomena are highly complex and require nonlinear boundaries for the rules. In this study, we tested the support vector machines (SVM) as a method for constructing nonlinear transition rules for CA. SVM is good at dealing with nonlinear complex relationships. Its basic idea is to project input vectors to a higher dimensional Hilbert feature space, in which an optimal classifying hyperplane can be constructed through structural risk minimization and margin maximization. The optimal hyperplane is unique and its optimality is global. The proposed SVM-CA model was implemented using Visual Basic, ArcObjects®, and OSU-SVM. A case study simulating the urban development in the Shenzhen City, China demonstrates that the proposed model can achieve high accuracy and overcome some limitations of existing CA models in simulating complex urban systems.

PARALLELIZING THREE DIMENSIONAL CELLULAR AUTOMATA WITH OpenMP

This paper describes our research on using Genetic Programming to obtain transition rules for Cellular Automata, which are one type of massively parallel computing system. Our purpose is to determine the existence of a limit of chaos for three dimensional Cellular Automata, empirically demonstrated for the two dimensional case. To do so, we must study statistical properties of 3D Cellular Automata over long simulation periods. When dealing with big three dimensional meshes, applying the transition rule to the whole structure can become a extremely slow task. In this work we decompose the Automata into pieces and use OpenMp to parallelize the process. Results show that using a decomposition procedure, and distributing the mesh between a set of processors, 3D Cellular Automata can be studied without having long execution times.

Simulating complex urban development using kernel-based non-linear cellular automata

Cellular automata (CA) have been increasingly used to simulate complex urban systems. Empirical data can be used to calibrate CA models so that realistic urban patterns can be generated. Traditionally, the calibration procedure employs linear regression methods, e.g., multicriteria evaluation. However, the evolution of urban systems often manifests the complexity of non-linear features, for which the linear transition rules are insufficient. This paper proposes to use the kernel-based learning techniques to acquire non-linear transition rules for CA. The kernel-based approach maps the original data vectors to an implicit high-dimensional feature space, through which complex non-linear problems are translated into simple linear problems. Compared with a widely used non-linear method, neural network, the kernel method is more mathematically “transparent” and therefore the results are easier to be analyzed. A case study of simulating the expansion of Guangzhou, a fast growing city in China, shows that the kernel-based CA even achieves a slightly higher accuracy than a neural-network-based CA.

Discovery of transition rules for geographical cellular automata by using ant colony optimization

A new intelligent algorithm of geographical cellular automata (CA) based on ant colony optimization (ACO) is proposed in this paper. CA is capable of simulating the evolution of complex geographical phenomena, and the core of CA models is how to define transition rules. However, most of the transition rules are defined by mathematical equations, and are hence not explicit. When the study area is complicated, it is much more difficult to extract parameters for geographical CA. As a result, ACO is applied to geographical CA to automatically and intelligently obtain transition rules in this paper. The transition rules extracted by ACO are defined as logical expressions rather than implicit mathematical equations to describe the complex relationships of the nature, and easy for people to understand. The ACO-CA model was applied to simulating rural-urban land conversions in Guangzhou City, China, and appropriate simulation results were generated. Compared with See5.0 decision tree model, ACO-CA is more suitable to discovering transition rules for geographical CA.

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.