Genetic Algorithms for the Calibration of Cellular Automata Urban Growth Modeling

This paper discusses the use of genetic algorithms to enhance the efficiency of transition rule calibration in cellular automata urban growth modeling. The cellular automata model is designed as a function of multitemporal satellite imagery and population density. Transition rules in the model identify the required neighborhood urbanization level for a test pixel to develop to urban. Calibration of the model is initially performed by exhaustive search, where the entire solution space is examined to find the best set of rule values. This method is computationally extensive and needs to consider all possible combinations for the transition rules. The rise in the number of variables will exponentially increase the time required for running and calibrating the model. This study introduces genetic algorithms as an effective solution to the calibration problem. It is shown that the genetic algorithms are able to produce modeling results close to the ones obtained from the exhaustive search in a time effective manner. Optimal rule values can be reached within the early generations of genetic algorithms. It is expected that genetic algorithms will significantly benefit urban modeling problems with larger set of input data and bigger solution spaces. Introduction Calibration in cellular automata urban growth modeling is to find the best combination of transition rule values such that the modeled urban phenomena can match the real one. Only through calibration can the cellular automata model produce an urban level and urban pattern close enough to reality. Calibration is critical in validating the performance of a designed cellular automata model (Batty and Xie, 1994a and 1994b; Batty et al., 1999; Landis and Zhang, 1998) and remains to be a challenge. It has been neglected until recent efforts to develop cellular automata as a reliable process for urban development simulation (Wu, 2002). It is shown (Li and Yeh, 2002; Wu, 2002) that urban cellular automata models are sensitive to transition rules and their parameter values. The practical difficulty in calibrating cellular automata rules is due to the large search space and its exponential rise when more variables and larger variable ranges are involved in the transition rules. A number of cellular automata calibration methods have been developed for urban growth modeling. They achieved various levels of success and efficiency. The structure of a calibration algorithm is mainly dependent on the design of the cellular automata model. Reviewing the existing calibration schemes shows various calibration styles. Genetic Algorithms for the Calibration of Cellular Automata Urban Growth Modeling Jie Shan, Sharaf Alkheder, Jun Wang Statistical, visual, and artificial intelligence tools (e.g., neural networks) have been used for calibration. Clarke et al. (1997 and 1998) calibrated the SLEUTH model by using visual and statistical tests to find the best values for the five growth parameters. Such tests were repeated for each parameter set in coarse, fine, and final phases. This calibration process took extended CPU time to reach the most appropriate parameter set in the search space (Yang and Lo, 2003). Wu and Webster (1998) defined the cellular automata transition rules using the multi-criteria evaluation (MCE) method. The objective of calibration in their model was to find the best weight factors for the input variables to match the real urban growth. Neural networks were used by Li and Yeh (2002) to calibrate the cellular automata model. A training set representing different combinations of parameter values and their corresponding modeling output were used to train the network to reproduce the desired urban pattern. The calibration in Wu (2002) estimated the probability of a particular state transition occurring at a location through a function of the development factors to balance the development probability, threshold, and allowed land consumption to reproduce the urban growth pattern. One of the recent studies in cellular automata model calibration is based on genetic algorithms. Genetic algorithms use the biological principles to direct the search towards regions (sub-space) of the solution space with likely improvement (Goldberg, 1989). Initial efforts tried to attach genetic algorithms to cellular automata urban model design for performance improvement. Colonna et al. (1998) modeled the changes in land-use for Rome, Italy through using genetic algorithms to produce a new set of rules for the cellular automata model. Genetic algorithms were used to find the optimal set of possibilities of land-use planning for Provo, Utah (Balling et al., 1999). Wong et al. (2001) used genetic algorithms for the primordial Lowry model in an attempt to choose the parameters of household and employment distribution for Hong Kong. A recent study tried to formalize genetic algorithms as a calibration tool for the SLEUTH model (Goldstein, 2003). The calibration results of the genetic algorithms were compared with the traditional, exhaustive search method through designing a comparison measure (metric of fit) as the product of three spatial metrics: the number of urban pixels, the number of urban clusters, and the Lee-Sallee index (Lee and Salle, 1970). This work was a good start towards formalizing the calibration process in cellular automata modeling; however, further improvements are PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING Oc t obe r 2008 1267 Geomatics Engineering, School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907 ([email protected]). Photogrammetric Engineering & Remote Sensing Vol. 74, No. 10, October 2008, pp. 1267–1277. 099-1112/08/7410-1267/$3.00/0 © 2008 American Society for Photogrammetry and Remote Sensing SA-AI-07.qxd 11/9/08 9:38 AM Page 1267