A mixed integer programming formulation and solution for traffic analysis zone delineation considering zone amount decision

Due to the spatial aggregation effect, the amount of zones (AoZ) has a direct influence on the optimality of traffic analysis zone delineation (TAZD) problems. Unlike existing studies, this paper addresses a TAZD problem in which both the AoZ and zone partitions are optimized. For the TAZD problem, we propose a mixed integer programming (MIP) model with the optimization objective of minimizing the sum of geographical errors within each zone. To solve the TAZD model, the following works have been done. First, the TAZD model is strengthened by our proposed IR (influence region) construction algorithm. Second, based on the strengthened model, we analyse the lower bound of the optimal AoZ from the theoretical perspective, and then the DRMI (domain reduction method I) is proposed to specify a tighter lower bound. Also, to reduce the amount of decision variables, we put forward the DRMII (domain reduction method II) which enumerates all feasible AoZ values. Third, to settle a non-solution situation, we propose the AHCBHA (aggregation hierarchical clustering based heuristic algorithm) in order to rebuild the solution space. Fourth, we then design two methods to solve the TAZD model. The former method combines the AHCBHA with the DRMI and the latter method combines the AHCBHA with the DRMII. Finally, the performance of the proposed TAZD and the developed methods is explored using a numerical example and a real-world case. The obtained results constitute good solutions.