偏离固定线路的微公交网络规划与运营的双重分解算法
A Double Decomposition Algorithm for Network Planning and Operations in Deviated Fixed-route Microtransit
AI总结：
本文针对偏离固定线路的微公交系统，构建两阶段随机整数优化的MiND模型，提出结合Benders分解与子路径列生成的双重分解算法，经曼哈顿真实数据验证可高效求解大规模算例，实现多维度出行共赢并提供开源实现。
摘要：
微公交结合了公共交通的可靠性与拼车的灵活性，为提升城市出行服务提供了契机。本文针对依托参考线路、可根据乘客需求按需偏离的偏离固定线路微公交系统，优化其设计与运营方案。我们通过两阶段随机整数优化构建了微公交网络设计（Microtransit Network Design，MiND）模型，第一阶段为网络设计与服务调度结构，第二阶段为车辆路径规划结构。我们利用负载扩展网络中基于子路径的微公交运营表示，推导出紧的第二阶段松弛形式。我们提出了结合Benders分解与基于子路径的列生成的双重分解算法，证明该算法能保持有效的最优性间隙，且可在有限次迭代内收敛到最优解。基于曼哈顿真实数据的实验结果表明，该方法可扩展至原本难以求解的大规模算例，最多支持10-100条候选线路与数百个站点。与公共交通、拼车模式的对比显示，微公交可在高效出行（高需求覆盖率、低成本、高服务水平）、公平出行（广泛的地理覆盖范围）和可持续出行（有限环境足迹）方面实现共赢。我们提供了开源实现以支持研究复现。
英文摘要：
Microtransit offers opportunities to enhance urban mobility by combining the reliability of public transit and the flexibility of ride-sharing. This paper optimizes the design and operations of a deviated fixed-route microtransit system that relies on reference lines but can deviate on demand in response to passenger requests. We formulate a Microtransit Network Design (MiND) model via two-stage stochastic integer optimization, with a first-stage network design and service scheduling structure and a second-stage vehicle routing structure. We derive a tight second-stage relaxation using a subpath-based representation of microtransit operations in a load-expanded network. We develop a double-decomposition algorithm combining Benders decomposition and subpath-based column generation. We prove that the algorithm maintains a valid optimality gap and converges to an optimal solution in a finite number of iterations. Results obtained with real-world data from Manhattan show that the methodology scales to large and otherwise-intractable instances, with up to 10-100 candidate lines and hundreds of stops. Comparisons with transit and ride-sharing suggest that microtransit can provide win-win outcomes toward efficient mobility (high demand coverage, low costs, high level of service), equitable mobility (broad geographic reach) and sustainable mobility (limited environmental footprint). We provide an open-source implementation to enable replication.
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