关键词: 城市交通, 需求响应公交, 机会约束模型, 模块化公交, 自适应大邻域搜索算法, 车内换乘

Abstract: This paper addresses the static scheduling optimization problem of demand-responsive modular bus systems under stochastic travel times. A chance-constrained programming model is developed, integrating route planning, passenger assignment, platooning, and in-motion transfer decisions. The stochastic model is equivalently reformulated as a mixed-integer second-order cone programming (MISOCP) model via deterministic transformation. To enable an efficient solution, an adaptive large neighborhood search (ALNS) algorithm is designed with embedded platooning and transfer search strategies, augmented by periodic local search to enhance global optimization performance. A case study is conducted with the real travel demand data from Shijingshan District, Beijing. The results demonstrate that the proposed scheduling strategy can effectively adapt to stochastic travel time environments and exhibit strong collaborative platooning capabilities. Compared with the conventional demand responsive transit operations, the proposed strategy reduces the total system cost by approximately 4.47% and the vehicle operating cost by approximately 5.85%. Sensitivity analyses are further performed to systematically examine the impacts of bus capacity, confidence level, and the travel time variability on scheduling decisions. The findings reveal that the bus capacity should be configured to strike a balance between reducing operating costs and maintaining passenger service quality. Increasing the confidence level of the chance constraints enhances on-time arrival reliability but incurs higher operating costs, while ignoring travel-time stochasticity systematically underestimates operational risks. In contrast, accounting for stochasticity enables an effective trade-off between service reliability and economic efficiency. This study provides theoretical foundations and practical decision-making support for the robust scheduling design of modular bus systems under uncertainty.

Key words: urban transportation, demand-responsive bus, chance-constrained model, modular bus, ALNS, in-motion transfer