The mean-standard deviation shortest path problem (MSDSPP) incorporates the travel time variability into the routing optimization. The idea is that the decision-maker wants to minimize the travel time not only on average, but also to keep their variability as small as possible. Its objective is a linear combination of mean and standard deviation of travel times. This study focuses on the problem of finding the best-\(K\) optimal paths for the MSDSPP. We denote this problem as the KMSDSPP. When the travel time variability is neglected, the KMSDSPP reduces to a \(K\)-shortest path problem with expected routing costs. This paper develops two methods to solve the KMSDSPP, including a basic method and a deviation path-based method. To find the \(k+1\)th optimal path, the basic method adds \(k\) constraints to exclude the first-\(k\) optimal paths. Additionally, we introduce the deviation path concept and propose a deviation path-based method. To find the \(k+1\)th optimal path, the solution space that contains the \(k\)th optimal path is decomposed into several subspaces. We just need to search these subspaces to generate additional candidate paths and find the \(k+1\)th optimal path in the set of candidate paths. Numerical experiments are implemented in several transportation networks, showing that the deviation path-based method has superior performance than the basic method, especially for a large value of \(K\). Compared with the basic method, the deviation path-based method can save 90.1% CPU running time to find the best \(1000\) optimal paths in the Anaheim network.

平均标准差最短路径问题 (MSDSPP) 将行程时间变化纳入路线优化中。这个想法是，决策者不仅希望平均旅行时间最小化，而且还希望保持尽可能小的变化。其目标是行程时间平均值和标准差的线性组合。本研究重点关注为 MSDSPP寻找最佳\(K\)条最优路径的问题。我们将此问题表示为 KMSDSPP。当忽略行程时间变化时，KMSDSPP 简化为具有预期路由成本的\(K\)最短路径问题。本文提出了两种求解KMSDSPP的方法，包括基本方法和基于偏差路径的方法。为了找到第\(k+1\)条最优路径，基本方法添加\(k\)条约束来排除第\(k\)条最优路径。此外，我们引入了偏差路径的概念并提出了一种基于偏差路径的方法。为了找到第\(k+1\)条最优路径，包含第\(k\)条最优路径的解空间被分解为多个子空间。我们只需要搜索这些子空间来生成额外的候选路径，并找到候选路径集中的第\(k+1\)条最优路径。在多个交通网络中进行的数值实验表明，基于偏差路径的方法比基本方法具有更优越的性能，特别是对于较大的\(K\)值。与基本方法相比，基于偏差路径的方法可以节省90.1%的CPU运行时间来找到阿纳海姆网络中最好的\(1000\)最优路径。