Part of the book: Cellular Automata
Part of the book: Emerging Applications of Cellular Automata
Although cellular automata (CA) offer a modelling framework and set of techniques for modelling the dynamic processes of urban growth, determining the optimal value of weights or parameters for elements or factors of urban CA models is challenging. This chapter demonstrates the implementation of a calibration module in a fuzzy cellular urban growth model (FCUGM) for optimizing the weights and parameters of an urban CA model using three types of algorithms: (i) genetic algorithm (GA), (ii) parallel simulated annealing (PSA) and (iii) expert knowledge (EK). It was found that the GA followed by EK produced better and more accurate and consistent results compared with PSA. This suggests that the GA was able to some extent to understand the urban growth process and the underlying relationship between input factors in a way similar to human experts. It also suggests that the two algorithms (GA and EK) have similar agreement about the efficiency of scenarios in terms of modelling urban growth. In contrast, the results of the PSA do not show results corresponding to those of the GA or EK. This suggests that the complexity of the urban process is beyond the algorithm’s capability or could be due to being trapped in local optima. With this satisfactory calibration of the FCUGM for the urban growth of Riyadh city in Saudi Arabia by using CALIB-FCUGM, these calibrated parameters can be passed into the SIM-FCUGM to simulate the spatial patterns of urban growth of Riyadh.
Part of the book: Applications of Spatial Statistics
Urban growth occurs in conjunction with a series of decision-making processes and is, on the whole, not deterministic but rather is the outcome of competing local demands and uncontrolled, chaotic processes. Fuzzy sets theory is ideally suited to treat the complexity and uncertainties in the decision-making process. This chapter presented an example of how fuzzy sets can be applied to model urban growth driving forces within geographical information system environment. The mathematical models for measuring, computing and defining 10 fuzzy urban growth factors to form fuzzy driving forces of urban growth in Riyadh City, Saudi Arabia, were discussed. Four factors were considered as the driving forces for urban growth in Riyadh City: the transport support factor, urban agglomeration and attractiveness factor, topographical constraints factor, and planning policies and regulations factor. The urban growth factors were established using fuzzy set theory, which quantified the effect of distance decay using fuzziness. This approach is a transparent method of interpreting the curve of distance decay using linguistic variables. This feature does not exist in the linear, negative exponential or inverse power functions. The results indicate that fuzzy accessibility and fuzzy urban density factors are capable of mimicking and representing the uncertainty in the behaviour of the human decision-making process in land development in a very efficient manner.
Part of the book: Spatial Analysis, Modelling and Planning