Measuring the additive border effect on cycling behaviours using particle swarm optimization

Understanding and improving the activity space borders is essential to facilitating human mobility. With the development of big data and network analysis methods, the study of borders has regained the interest of various communities. However, the previous model used logarithmic linear regression to analyze the border effect as multiplying by the physical distance, and this was contrary to the actual concept that each additional border should contribute cumulatively to the overall travel resistance. At the same time, cycling as a low-carbon and non-motorized transportation mode, is sensitive to the geometric attribute of physical border, which is ignored in the current models. This research proposes a Particle Swarm-Additive Border Effect Model (PSO-ABEM) to measure the additive barriers effect of physical borders on cycling behaviours considering borders' geometric attributes. The case study in Longgang, Shenzhen exhibits the high interpretability of the proposed PSO-ABEM. The result indicates the average additive 14.3 % cycling resistance for each additional physical border, as well as the geometry-sensitive impact of physical borders on cycling travel. The findings also reveal the non-linear or U-like shape effects of physical borders on cycling behaviours: medium-distance trips have the thinnest border thickness, short-distance trips have the medium one, and the long-distance trips have the thickest thickness. Conducting more precise analyses of border effects can offer valuable guidance for urban planning.