Applying optimization algorithms for spatial estimation of travel demand variables

Using spatial statistics techniques is a way to improve the forecast of travel demand variables considering their spatial dependence. The semivariogram is a proper geostatistic tool for represent the spatial structure of a Regionalized Variable. Therefore, the semivariogram modeling is a fundamental step and is often done visually, based on data knowledge and researchers’ experience, as well as taking into account automatic criteria, such as weighted least squares function. Moreover, these automatic procedures generally assume that data distribution is Gaussian. This research aims to evaluate the combined use of Genetic Algorithms (GAs) and geostatistical methods to forecast travel demand variables, in order to optimize the calculation and fitting of semivariograms. Car Trip rates and Income by household were estimated using the GA application in variographic models, and therefore enabled us to obtain numerous semivariogram parameters. Consequently, intervals of the most frequent parameters were obtained and those with better performance (based on the fitness value) were chosen to carry out the modeling procedure using geostatistical software. The geostatistical modeling optimization procedure, proposed in this study, was validated considering not only a non spatial model (traditional Linear Regression) but also a different spatial approach, the Geographically Weighted Regression (GWR). The validation was carried out using a bivariate example. Thus, the procedure enabled us to compute and fit semivariograms more accurately, contributing to knowledge about spatial structure and variographic parameters related to almost optimal solutions. It is important to consider that the code developed from this article is available for applications in other knowledge areas with spatial dependence data