Abstract Aiming to increase successful transfers at stations for late-night passengers, we first propose an efficient dwell time adjustment strategy for the last-train coordination planning problem under transfer-passenger flows uncertainty. Unlike the traditional robust optimization model, we present a novel distributionally robust chance-constrained program to model this problem, where the probability distributions of the uncertain parameters are only partially available. By introducing a pessimistic ambiguous chance constraint, the proposed distributionally robust model guarantees that the probability of satisfying the service-oriented objective, i.e., maximum successful transfer-passenger flows in the whole subway system is larger than a predetermined confidence level in the worst case. We then draw the connection of the distributionally robust model with the traditional robust optimization model, and show that the proposed model can be interpreted as a generalized version of the robust optimization model. We further propose a safe tractable approximation method to reformulate the original model as a mixed-integer second-order conic programming under the bounded-perturbation ambiguous set, which can be solved to optimality on only small instances by the CPLEX. Hence, we develop a tabu search heuristic algorithm to obtain high-quality solutions for large-sized instances. We also use local search as a baseline algorithm to observe the improvements of the tabu search algorithm. Finally, we illustrate the superiority of the developed model on the Nanjing and Beijing subway networks and compare the performance of the proposed algorithms.

中文翻译：

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具有驻留时间调整策略的分布鲁棒末班车协调规划问题

摘要 为了提高深夜乘客车站换乘成功率，我们首先针对换乘-客流不确定性下的末班车协调规划问题提出了一种有效的停留时间调整策略。与传统的鲁棒优化模型不同，我们提出了一种新颖的分布鲁棒机会约束程序来模拟这个问题，其中不确定参数的概率分布仅部分可用。通过引入悲观模糊机会约束，所提出的分布鲁棒模型保证满足服务导向目标的概率，即在最坏情况下，整个地铁系统中的最大成功换乘客流大于预定的置信水平。然后，我们绘制了分布鲁棒模型与传统鲁棒优化模型的联系，并表明所提出的模型可以解释为鲁棒优化模型的广义版本。我们进一步提出了一种安全易处理的近似方法，将原始模型重新表述为有界微扰模糊集下的混合整数二阶圆锥规划，CPLEX 可以仅在小实例上将其求解为最优。因此，我们开发了一种禁忌搜索启发式算法，以获得大型实例的高质量解决方案。我们还使用局部搜索作为基线算法来观察禁忌搜索算法的改进。最后，