Calibration of cellular automata models using differential evolution to simulate present and future land use

Abstract

A key issue in cellular automata (CA) modeling is the minimization of the differences between the actual and simulated patterns, which can be mathematically formulated as an objective function. We develop a new hybrid model (termed DE-CA) by integrating differential evolu-

Urban Growth Modeling and Future Scenario Projection Using Cellular Automata (CA) Models and the R Package Optimx

“…The overall probability is compared to a pre-defined threshold to determine if a non-urban cell can transform its state. The decision rule is [17,33]:…”

“…The metaheuristics were processed based on a fitness function representing the residuals in fitting the relationships between urban growth and its drivers. The fitness function can be given by [17,34]:…”

“…Metaheuristics are partial-search artificial intelligence algorithms that are capable of minimizing residuals when defining near-optimal CA parameters [15,16], ultimately achieving more accurate simulations. For CA model calibration, metaheuristics are superior because they incorporate complex real-world constraints in the optimization procedure through mathematically expressed equalities and/or inequalities [17], allowing metaheuristics to search for alternative CA parameters in future scenario prediction.…”

“…These algorithms originated in simulating natural phenomena corresponding to complex optimization [20,24,25]. They guide the optimization using a fitness function, which is typically built on the deviations (residuals) between the actual classifications and the simulation results [17]. Each metaheuristic has a different internal scheme to guide optimization [26], and most metaheuristics do not require differentiation of the fitness function.…”

“…CA transition rules have commonly been presented in three forms: (1) "if-then" and/or "what-if" rules that denote cell state transformation from non-urban to urban if one of the transition rules is met [23,27,28], (2) factor-weighted transition rules that calculate the probability of each non-urban cell transforming to an urban cell [17,20], and (3) black-box transition rules that do not clearly show the cell transformation procedure [24,29]. Artificial neural networks (ANNs) generate transition rules using black-box methods; metaheuristics such as ACO and CS create the transition rules through "if-then"/"what-if" rules; SA, GPS, PSO, GA, DE, BA, and ABC express transition rules with mathematical formulae similar to those derived from LR.…”