基于混合整数非线性规划的接驳公交优化模型

接驳公交线路设计与运营方案优化是轨道交通与地面公交协同发展的研究课题之一，本文分析其在模型构建、规划方法及模型算法等研究方面的不足。以问题为导向，构建基于混合整数非线性规划的接驳公交协同优化模型，通过对模型重构进行求解。并通过实例分析验证模型和算法的有效性。结果发现：第一，以往研究中将线路设计与运营方案协同优化模型较少，本文统筹考虑接驳公交线路设计和发车频率优化构建模型；第二，以往研究中大多考虑多条接驳公交线路与1个轨道站点连接的单一目的地模式，本文通过增加“多对多”约束条件，使模型更加符合现实需求分配；第三，针对混合整数非线性模型求解困难的问题，本文通过模型重构，降低了计算 复杂度；第四，研究实例基于2个轨道站点和17个接驳公交需求点，得到2条接驳线路和相应发车频率，并通过与相同拓扑路网下应用深度优先搜索算法(DFS)求解结果进行对比分析，验证了本文所建协同优化模型的可行性和有效性。

Feeder Bus Routes and Frequency Optimization Based on Mixed Integer Nonlinear Programming

The optimization of feeder bus in terms of network design and frequency setting is an important topic about the coordinated development of rail transit and ground transit. This paper analyzes the model construction, planning methods, and model algorithms deficiencies in previous studies. The study develops an optimization model for feeder bus operations based on the mixed integer nonlinear programming, and the model is solved by reconstructions. Then, the model and algorithm are verified through case analysis. The results showed that: The proposed model in this study includes a multiple to multiple (M to M) constraint, which is closer to the real transit operation conditions. Compared to the Depth-first search (DFS) algorithm using the same topology road network, the proposed model reduces the calculation complexity and is feasible and effective in optimizing the feeder bus routes and departure frequencies