Modelling built-up expansion and densification with multinomial logistic regression, cellular automata and genetic algorithm

This paper presents a model to simulate built-up expansion and densification based on a combination of a non-ordered multinomial logistic regression (MLR) and cellular automata (CA). The probability for built-up development is assessed based on (i) a set of built-up development causative factors and (ii) the land-use of neighboring cells. The model considers four built-up classes: non built-up, low-density, medium-density and high-density built-up. Unlike the most commonly used built-up/urban models which simulate built-up expansion, our approach considers expansion and the potential for densification within already built-up areas when their present density allows it. The model is built, calibrated, and validated for Wallonia region (Belgium) using cadastral data. Three 100 × 100 m raster-based built-up maps for 1990, 2000, and 2010 are developed to define one calibration interval (1990–2000) and one validation interval (2000 − 2010). The causative factors are calibrated using MLR whereas the CA neighboring effects are calibrated based on a multi-objective genetic algorithm. The calibrated model is applied to simulate the built-up pattern in 2010. The simulated map in 2010 is used to evaluate the model's performance against the actual 2010 map by means of fuzzy set theory. According to the findings, land-use policy, slope, and distance to roads are the most important determinants of the expansion process. The densification process is mainly driven by zoning, slope, distance to different roads and richness index. The results also show that the densification generally occurs where there are dense neighbors whereas areas with lower densities retain their densities over time.