This paper focuses on a specific stochastic shortest path (SSP) problem, namely the punctuality problem. It aims to determine a path that maximizes the probability of arriving at the destination before a specified deadline. The popular solution to this problem always formulates it as a cardinality minimization problem by considering its data-driven nature, which is approximately solved by the 1 , -norm relaxation. To address this problem accurately, we consider the special character in the cardinality-based punctuality problem and reformulate it by introducing additional variables and constraints, which guarantees an accurate solution. The reformulated punctuality problem can be further transformed into the standard form of integer linear programming (ILP), thus, can be efficiently solved by using the existing ILP solvers. To evaluate the performance of the proposed solution, we provide both theoretical proof of the accuracy, and experimental analysis against the baselines. Particularly, the experimental results show that in the following two scenarios, 1) artificial road network with simulated travel time, 2) real road network with real travel time, our accurate solution works better than others regarding the accuracy and computational efficiency. Furthermore, three ILP solvers, i.e., CBC, GLPK and CPLEX, are tested and compared for the proposed accurate solution. The result shows that CPLEX has obvious advantage over others.

中文翻译：

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基于基数的准点问题的精确解

本文重点研究一个特定的随机最短路径（SSP）问题，即准点问题。它旨在确定一条在指定期限之前到达目的地的概率最大化的路径。这个问题的流行解决方案总是通过考虑其数据驱动的性质将其表述为基数最小化问题，这可以通过 1 , -范数松弛来近似解决。为了准确地解决这个问题，我们考虑了基于基数的准点问题中的特殊性，并通过引入额外的变量和约束来重新表述它，以保证准确的解决方案。重新表述的守时问题可以进一步转化为整数线性规划 (ILP) 的标准形式，从而可以使用现有的 ILP 求解器有效地解决。为了评估所提出的解决方案的性能，我们提供了准确性的理论证明和针对基线的实验分析。特别是，实验结果表明，在以下两种情况下，1）模拟旅行时间的人工路网，2）真实旅行时间的真实路网，我们的精确解决方案在准确性和计算效率方面比其他方案更有效。此外，三个 ILP 求解器，即 CBC、GLPK 和 CPLEX，被测试和比较，以获得所提出的准确解决方案。结果表明，CPLEX 具有明显的优势。1) 模拟旅行时间的人工路网，2) 真实旅行时间的真实路网，我们的精确解决方案在准确性和计算效率方面比其他解决方案更有效。此外，三个 ILP 求解器，即 CBC、GLPK 和 CPLEX，被测试和比较，以获得所提出的准确解决方案。结果表明，CPLEX 具有明显的优势。1) 模拟旅行时间的人工路网，2) 真实旅行时间的真实路网，我们的精确解决方案在准确性和计算效率方面比其他解决方案更有效。此外，三个 ILP 求解器，即 CBC、GLPK 和 CPLEX，被测试和比较，以获得所提出的准确解决方案。结果表明，CPLEX 具有明显的优势。