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Article Excerpt
Introduction
A classical cellular automata (CA) model is a set of identical elements, called cells, each one of which is located in a regular, discrete space. Each cell can be associated with a state from a finite set. The model evolves in discrete time steps, changing the states of all its cells according to a transition rule, homogeneously and synchronously applied at every step. The new state of a certain cell depends on the previous states of a set of cells, which can include the cell itself, and constitutes its neighborhood.
Urban cellular automata (Urban-CA) are those cellular automata used to simulate and forecast land-use and land-cover change in urban areas. As a consequence of years of study, Urban-CA models have become much more complex than the original basic CA concepts. The neighborhood patterns, the transition rules, the linkages to other socio-economic models have all made Urban-CA advanced and intensive computing systems (Benenson and Torrens 2004).
One of the most important features of CA is that models can be used to simulate complex dynamic spatial patterns through a set of simple transition rules. However, several spatial factors, which have impact on urban development, should be considered while simulating a real geo-spatial phenomenon. Usually, in a model, these spatial factors are indicated by a set of parameters that reflect the contributions of corresponding factors to the model. Previous studies have discovered that model parameters have significant impact on the simulation results of CA models (Wu and Webster 1998). Thus, calibration processes are needed to determine the appropriate parameter values so that CA models can produce more realistic simulation results.
In practice, many variables, even hundreds of them, could be used to simulate a complex spatial system (White and Engelen 1994), most linked by non-linear relationships. After decades of study, the calibrating methods have become one of the most crucial components of geographic/urban CA models. One popular calibration method was developed by Clarke and Gaydos (1998) for a CA-based urban growth model called SLEUTH. SLEUTH is a CA model of urban growth and land use (LU) change which couples two CAs together and calibrates for historical time sequences using Geocomputational methods (Silva and Clarke 2002). This method uses the computer to produce simulation results using different combinations of parameter values, and then compares each result with real historical data to determine the best matching combination. However, since there could be an enormous number of combinations of parameter values, this calibration process is extremely time-consuming. Actually, even with high-performance workstations, it takes hundreds, even thousands, of hours to calibrate the model in practice. Furthermore, the computing time would extend exponentially if more variables were involved. Another method is to set the parameter values according to experts' experiences or a hypothesis. Obviously, this method is very subjective and unreliable.
In this paper, an artificial neural network (ANN) is proposed as a solution to the constraints of CA model calibration. The ANN, simulating a human brain neural network, has been used to simulate complex systems, including geo-spatial dynamic phenomena (Openshaw, et al. 1998). A neural network can learn from available data, and deal with redundancy, inaccuracy, and noise. Knowledge and experience can be easily learned and stored for further simulation. Thus, integrating ANN into CA will significantly reduce the computing time of calibration. In addition, CA models will benefit from the ANN's capacity of dealing with non-linear systems in terms of simulating and forecasting complex dynamic geo-spatial systems (Li and Yeh 2002).
Another important issue of Urban-CA research is how to model the interaction between socio-economic factors and the development of an urban area. Many studies have shown that socio-economic factors, including government, police, planning, economic development, and population growth play important roles in the process of urban development. More and more researchers try to model these relationships in their Urban-CA models. Usually there are two approaches: loose integration and internal merging. Using the loose integration approach, one or more stand-alone socio-economic models are linked with the CA model through parameter exchange or linking functions. These socio-economic models act as external factors interacting with the CA model. Using the internal merge approach, socio-economic factors are involved in the CA model as non-spatial variables. Socio-economic factors...
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