一种面向带预测性维护的机车车辆周转问题的迭代求精方法
An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance
AI总结：
针对带预测性维护的机车车辆周转问题，提出基于状态扩展事件图与整数线性规划的对偶求解方法，通过迭代求精离散化实现收敛下界，并经测试实例验证了方法有效性。
摘要：
带预测性维护的机车车辆周转问题（RSRP-PdM）涉及为车队分配行程，同时结合基于车辆预测故障概率的集成维护调度。这些概率由车辆的健康状态决定，健康状态被视为服从参数化概率分布函数族的随机变量。在行程运行期间，相应的参数会得到更新。本文提出了一种求解RSRP-PdM的对偶方法，并将该问题基于线性规划的下界推广至多参数概率分布函数族。为此，我们定义了一个舍入函数，可实现对参数的一致低估，并通过状态扩展事件图对问题建模，其中可能的状态被限制在一个离散集合内。这衍生出一个通过整数线性规划求解的流问题。我们证明，对底层离散化进行迭代求精可得到从下方收敛到原始实例最优解的解。因此，所考虑的整数线性规划的线性松弛可给出RSRP-PdM的一个下界。最后，我们报告了在一组测试实例库上开展的计算实验结果。
英文摘要：
The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These probabilities are determined by the health states of the vehicles, which are considered to be random variables distributed by a parameterized family of probability distribution functions. During the operation of the trips, the corresponding parameters get updated. In this article, we present a dual solution approach for RSRP-PdM and generalize a linear programming based lower bound for this problem to families of probability distribution functions with more than one parameter. For this purpose, we define a rounding function that allows for a consistent underestimation of the parameters and model the problem by a state-expanded event-graph in which the possible states are restricted to a discrete set. This induces a flow problem that is solved by an integer linear program. We show that the iterative refinement of the underlying discretization leads to solutions that converge from below to an optimal solution of the original instance. Thus, the linear relaxation of the considered integer linear program results in a lower bound for RSRP-PdM. Finally, we report on the results of computational experiments conducted on a library of test instances.
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