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

Abstract

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.

Keywords:

• NSGA-II
• land conversion
• rural–urban
• cellular automata
• calibration
• Logit regression

Acknowledgments

The supports and comments from Dr. Hongxia Wang, Prof. Yee Leung, Prof. Michael Batty, Prof. Shaowen Wang, and Prof. Michael Goodchild on this research are gratefully acknowledged. We would also like to thank the anonymous reviewers for their valuable comments and suggestions.