Synchronous transfer has been widely studied in public transport scheduling, with most research focusing on coordination among conventional bus lines. However, with the rapid expansion of urban rail transit systems, metro–bus transfers have become increasingly important for enhancing overall urban public transport network performance. This study investigates the maximum synchronous transfer problem between metro and conventional bus services under passenger flow constraints. Considering the large transfer demand and the pulse-arrival characteristics of metro trains, a passenger waiting constraint at bus stops is incorporated to reflect capacity limitations and crowding effects. A passenger-flow-constrained maximum synchronization model is formulated to optimize bus departure times without increasing service frequency. Dongjiekou Metro Station and three surrounding pairs of bus stops are selected as a case study. Model parameters are determined through field surveys and operational data. The Grey Wolf Optimizer (GWO) and a simulated annealing–improved Grey Wolf Optimizer (SA-IGWO) are employed to solve the proposed model. The results show that both algorithms significantly improve synchronized transfer volumes by adjusting departure times without increasing service frequency. Compared with the original schedule, the SA-GWO achieves an improvement in synchronization performance ranging from 45% to 50%, outperforming the standard GWO.
Lan et al. (2026) studied this question.