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.

[1]  Fulong Wu,et al.  SimLand: A Prototype to Simulate Land Conversion Through the Integrated GIS and CA with AHP-Derived Transition Rules , 1998, Int. J. Geogr. Inf. Sci..

[2]  Liu Xiaoping,et al.  Case-based Cellular Automaton for Simulating Urban Development in a Large Complex Region , 2007 .

[3]  Kasper Kok,et al.  A method and application of multi-scale validation in spatial land use models , 2001 .

[4]  Li Xia,et al.  Genetic algorithms for determining the parameters of cellular automata in urban simulation , 2007 .

[5]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[6]  Guy Engelen,et al.  Cellular Automata as the Basis of Integrated Dynamic Regional Modelling , 1997 .

[7]  Ago Yeh,et al.  Constrained Cellular Automata for Modelling Sustainable Urban Forms , 1999 .

[8]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[9]  Fulong Wu,et al.  Calibration of stochastic cellular automata: the application to rural-urban land conversions , 2002, Int. J. Geogr. Inf. Sci..

[10]  Xiaoping Liu,et al.  An extended cellular automaton using case‐based reasoning for simulating urban development in a large complex region , 2006 .

[11]  A. Bregt,et al.  Revisiting Kappa to account for change in the accuracy assessment of land-use change models , 2011 .

[12]  Xia Li,et al.  Modelling sustainable urban development by the integration of constrained cellular automata and GIS , 2000, Int. J. Geogr. Inf. Sci..

[13]  Michael Batty,et al.  Modelling and prediction in a complex world , 2005 .

[14]  Keith C. Clarke,et al.  Loose-Coupling a Cellular Automaton Model and GIS: Long-Term Urban Growth Prediction for San Francisco and Washington/Baltimore , 1998, Int. J. Geogr. Inf. Sci..

[15]  Li Zhang,et al.  Spatiotemporal analysis of rural–urban land conversion , 2009, Int. J. Geogr. Inf. Sci..

[16]  Roger White,et al.  Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns , 1993 .

[17]  Ming Zhang,et al.  The Second Generation of the California Urban Futures Model. Part 2: Specification and Calibration Results of the Land-Use Change Submodel , 1998 .

[18]  F. Wu,et al.  Simulation of Land Development through the Integration of Cellular Automata and Multicriteria Evaluation , 1998 .

[19]  Michael Batty,et al.  From Cells to Cities , 1994 .

[20]  Xia Li,et al.  Dynamic transition rules for geographical cellular automata , 2008, Geoinformatics.

[21]  Michael Batty,et al.  Urban Evolution on the Desktop: Simulation with the Use of Extended Cellular Automata , 1998 .

[22]  Anthony Gar-On Yeh,et al.  Neural-network-based cellular automata for simulating multiple land use changes using GIS , 2002, Int. J. Geogr. Inf. Sci..

[23]  G. Rabino,et al.  Learning Urban Cellular Automata In A Real World , 1998 .

[24]  G..  A Comparison of Sampling Schemes Used in Generating Error Matrices for Assessing the Accuracy of Maps Generated from Remotely Sensed Data , 2008 .

[25]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[26]  E. Silvaa,et al.  Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal , 2002 .

[27]  William Rand,et al.  Path dependence and the validation of agent‐based spatial models of land use , 2005, Int. J. Geogr. Inf. Sci..

[28]  Elisabete A. Silva,et al.  Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal , 2002 .

[29]  Noah Goldstein,et al.  Brains Vs. Brawn – Comparative Strategies For The Calibration Of A Cellular Automata – Based Urban Growth Model , 2003 .

[30]  Michael Batty,et al.  Modelling Inside GIS: Part 2. Selecting and Calibrating Urban Models Using ARC-INFO , 1994, Int. J. Geogr. Inf. Sci..

[31]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[32]  Yongjiu Feng,et al.  A heuristic cellular automata approach for modelling urban land-use change based on simulated annealing , 2013, Int. J. Geogr. Inf. Sci..

[33]  Xia Li,et al.  Cellular automata for simulating land use changes based on support vector machines , 2008, Comput. Geosci..

[34]  Michael Batty,et al.  Spatial multi-objective land use optimization: extensions to the non-dominated sorting genetic algorithm-II , 2011, Int. J. Geogr. Inf. Sci..

[35]  Jie Shan,et al.  Genetic Algorithms for the Calibration of Cellular Automata Urban Growth Modeling , 2008 .

[36]  Robert Gilmore Pontius,et al.  Comparison of the structure and accuracy of two land change models , 2005, Int. J. Geogr. Inf. Sci..

[37]  M. Batty,et al.  Modeling urban dynamics through GIS-based cellular automata , 1999 .

[38]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[39]  Keith C. Clarke,et al.  A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area , 1997 .

[40]  Susan Craw,et al.  Applying Genetic Algorithms to Multi-Objective Land Use Planning , 2000, GECCO.

[41]  Yongjiu Feng,et al.  An Optimised Cellular Automata Model Based on Adaptive Genetic Algorithm for Urban Growth Simulation , 2010, SDH.

[42]  Li Xia Yang Qing-sheng.  Calibrating urban cellular automata using genetic algorithms , 2007 .