基于分布鲁棒优化的城市轨道交通网络末班车衔接研究

Distributionally robust optimization for the last-train connection planning problem in urban rail transit networks

随着我国城市轨道交通网络规模快速扩张,线路间协调配合的高度复杂性给城市轨道交通的运营组织与管理带来极大挑战.针对客流需求及其分布双重不确定条件下的城市轨道交通网络末班车衔接优化问题,提出一种分布鲁棒机会约束规划模型,即在给定容忍度下最小化最坏条件下的换乘失败客流量.通过分析分布鲁棒优化模型与其对应鲁棒优化模型之间的联系,证明该模型为鲁棒优化模型的推广形式.基于有限的期望和方差信息构造高斯分布非精确集,采用对偶理论将原模型转化为可利用CPLEX求解的混合整数二阶锥规划形式,并通过数值实验验证所构建模型的有效性.算例结果表明:分布鲁棒模型对于小规模网络可利用CPLEX快速求得精确解;相比鲁棒模型可有效避免产生过于保守的优化结果;相比随机模型可有效降低极端情况下换乘失败客流量,具有较强的鲁棒性.

With the rapid development and expansion of the urban rail transit network in China,the coordination between different lines brings great challenges to the operation due to its high complexity.In order to minimize the unsuccessful transfer-passenger flows of last-train under the worse case with the given level of tolerance,a distribution ally robust chance-constrained programming model is proposed for the last-train connection planning problem in urban rail transit networks under uncertain transfer-passenger demand.In particular,the probability distribution of uncertain parameters is only partially known.By analyzing the relationship between the distributionally robust optimization model and the corresponding robust optimization model,it is proved that the former is an extension of the latter.Furthermore,the original model can be reformulated into a second-order mixed-integer conic programming form under the Gaussian perturbations ambiguity set based on the limited information of expectation and variance,which can be solved by CPLEX.The results of numerical examples indicate that the proposed model can be solved to optimality quickly by CPLEX on a small network,and can effectively avoid over-conservative solutions compared to the robust optimization model and reduce unsuccessful transfer-passenger flows in the extreme situation compared with the stochastic programming model,which exhibits more robust performance.