Abstract: This paper presents a bi-level mixed-integer program model to jointly optimize the urban rail and bus transit on a grid network. The model takes a variety of route types of passengers into consideration and solves the headway of the urban rail and bus and the line spacing and stop spacing of the bus system. The upper model is a continuous model aiming at minimizing the total system cost of the patrons and the transit agency. It is used to find the tradeoff relationship between passengers and operators, and deduce each cost in detail. The sequential quadratic programming algorithm is used and the convex algorithm is used to envelop the nonconvex problem. The lower model is a route assignment problem according to probability allocation, and the method of successive averages (MSA) algorithm is embedded to weighted allocate the flow of each route. Considering the non-convexity of the analytical form of the problem, the heuristic method is used to solve it. Finally, this paper takes an actual network in Jianye District of Nanjing as an example to verify the effectiveness of the model. Taking the peak period as an example, the average travel time of passengers in this study is reduced from 41.6 minutes to 33.0 minutes, which reduces by 20.6% through the model optimization. The proposed optimization model in this paper can provide a reference and basis for the planning of public transport networks in grid network cities.

Key words: urban traffic, joint optimization, continuum approximation, bimodal transit network

摘要： 为研究城市轨道交通与常规公交线网耦合优化设计问题，本文基于近似方格型路网并考虑乘客的多种路径选择，构建双层混合整数优化模型，以同时求解地铁与常规公交发车时距、常规公交的线间距及站间距。上层模型是以系统总成本(乘客成本与运营商成本之和)最小为目标的连续近似模型，以寻求乘客与运营商两者之间的平衡关系，并对各项成本进行详细推导。采用序列二次规划算法，并用凸算法对该非凸问题进行包络。下层为考虑依概率分配的路径分配问题，使用MSA算法对各路径流量加权分配，考虑到问题的解析形式具有非凸性，故采用启发式方法进行求解。最后，以南京市建邺区实际公交线网为例进行案例分析，以此验证该优化模型的有效性。经过优化，以非拥堵时段为例，该研究区域内乘客平均出行时间由 41.6 min减少至 33.0 min，降低约20.6%。本文所提出的优化模型可以为方格路网城市的公共交通线网规划提供参考依据。

关键词: 城市交通, 耦合优化, 连续近似, 双模式网络