Parameter Calibration of the Patch Growing Algorithm for Urban Land Change Simulations

Urban growth modelling is a current trend in geo-computation due to its impact on the local living environment and the quality of life. The FUTure Urban-Regional Environment Simulation (FUTURES) model produces projections of landscape patterns by coupling land suitability, per-capita demand, and patch growing algorithm (PGA) sub-models. In particular, the PGA is the urban growing simulator component that takes into account the stochastic nature of urban development. It requires a set of parameters, namely compactness mean, compactness range, and discount factor to approximate the general characteristics of the urban development structure. The fitness of the parameters is measured by computing the difference between the area and compactness histograms of the observed and simulated urban growths. On the one hand, the authors find these parameters via an exhaustive grid search; nevertheless, this requires evaluating all the points in the grid, which implies a high computational cost because each point is associated with several PGA simulations. In addition, the approximation is limited to be one of the points in the grid. Thus, the better the precision is, the higher the required computational cost. On the other hand, evolutionary algorithms have been widely used for the automatic calibration of parameters but, in general, they are not designed to use a low number of evaluations, require expert tuning, and to define the stop criteria. Therefore, we propose an algorithm to find the adequate parameters, with minimum expert intervention, using an Estimation of Distribution Algorithm designed to use a low number of function evaluations (EDALNFE) when compared to the grid search. EDALNFE provides several assets: it delivers competitive results, it requires a low number of function evaluations, it does not require expert settings, and it is equipped with an automatic stop criterion. The proposed algorithm is compared to exhaustive grid search (the only method readily available in the FUTURES package) and differential evolution to demonstrate its superior performance.