Abstract: The problem of optimal integration of macro network for urban transit is studied by mixed integer optimization. The optimal design modal is formulated by level of service between zones, transit capacity and travel demands. The multi-objective modal synthetically considers the optimization of transit construction cost, hubs construction cost and unit operation cost, which includes the cost of passengers total travel time, the investment cost, the energy cost and pollution cost, and computational approach of schemes is provided. The efficiency of solution is improved by branch-cut algorithm. The feasibility and effectiveness of the modal and the algorithm is testified by the experimental example, and it is showed that the optimal plan schemes for different development phases are discovered by the algorithm to meet requirement for different level of service. The results indicate that the model and solution should be a promising way to improve the macro network of urban transit.

Key words: urban traffic, transit system, macro-network, optimal integration, mixed-integer programming, branch-cut algorithms

摘要： 采用混合整数优化方法，研究城市公交系统宏观网络优化整合问题. 根据区域间服务水平要求、公交供给能力以及满足一定乘客出行要求，构造公交系统宏观网络优化整合多目标模型，该多目标函数考虑乘客总出行时间成本、各公交方式的建设总费用、各公交方式的能耗和污染物排放总费用、枢纽建设总费用最优；并给出最优解的多方案求解步骤；针对多节点采用Branch-Cut算法进行求解，提高求解效率；通过算例对模型和算法的可行性和有效性进行了验证，说明该算法可得出不同发展阶段下的公交宏观网络最优布局方案；结果表明，提出的模型与算法能对城市公交宏观网络布局提供辅助决策支持.

关键词: 城市交通, 公交系统, 宏观网络, 优化整合, 混合整数规划, 分支－切割算法