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.