Flexible buses provide on-demand services to one or more local communities in a specific geographical area. Bus routes can be adjusted dynamically according to real-time passenger demand in a cost-effective manner. This study investigated the dynamic bus-routing problem considering stochastic future passenger demand. A two-stage stochastic programming model was formulated to minimise the total vehicle travel time cost and penalty for rejecting requests. A rolling horizon scheme was adopted to handle the dynamic changes in passenger requests and vehicle routes. A vector-similarity-based clustering and adaptive large neighbourhood searching (VSC-ALNS) algorithm was developed to solve this problem. Vehicles and passengers were matched and clustered into groups based on vector similarity, and vehicle routes were generated using an adaptive large-neighbourhood search algorithm for each cluster. The effectiveness of the proposed method was evaluated in four cases with different demand intensities using Shanghai taxi order data. The results indicate that flexible buses are more suitable for moderate demand cases, ranging from 20 to 50 requests per square kilometre per hour.

灵活的公交车为特定地理区域的一个或多个当地社区提供按需服务。公交线路可以根据实时乘客需求以具有成本效益的方式动态调整。本研究调查了考虑随机未来乘客需求的动态公交路线问题。制定了一个两阶段随机规划模型，以最小化车辆总行程时间成本和拒绝请求的惩罚。采用滚动地平线方案来处理乘客请求和车辆路线的动态变化。开发了一种基于向量相似性的聚类和自适应大邻域搜索 (VSC-ALNS) 算法来解决该问题。车辆和乘客根据向量相似性进行匹配和聚类，和车辆路线是使用每个集群的自适应大邻域搜索算法生成的。使用上海出租车订单数据在四种不同需求强度的情况下评估所提出方法的有效性。结果表明，灵活的公交车更适合中等需求情况，范围为每平方公里每小时 20 到 50 次请求。