This paper presents an approach to shortest path minimization for graphs with random weights of arcs. To deal with uncertainty we use the following risk measures: Probability of Exceedance (POE), Buffered Probability of Exceedance (bPOE), Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR). Minimization problems with POE and VaR objectives result in mixed integer linear problems (MILP) with two types of binary variables. The first type models path, and the second type calculates POE and VaR functions. Formulations with bPOE and CVaR objectives have only the first type binary variables. The bPOE and CVaR minimization problems have a smaller number of binary variables and therefore can be solved faster than problems with POE or VaR objectives. The paper suggested a heuristic algorithm for minimizing bPOE by solving several CVaR minimization problems. Case study (posted at web) numerically compares optimization times with considered risk functions.

本文提出了一种具有最小弧度权重的图的最短路径最小化方法。为了处理不确定性，我们使用以下风险度量：超额概率（POE），超额缓冲概率（bPOE），风险价值（VaR）和条件风险价值（CVaR）。POE和VaR目标的最小化问题会导致带有两种类型的二进制变量的混合整数线性问题（MILP）。第一种类型对路径建模，第二种类型计算POE和VaR函数。具有bPOE和CVaR目标的配方仅具有第一类二进制变量。bPOE和CVaR最小化问题的二进制变量数量较少，因此比POE或VaR目标问题可以更快地解决。本文提出了一种启发式算法，可以通过解决一些CVaR最小化问题来最小化bPOE。案例研究（发布在网站上）将优化时间与考虑的风险函数进行了数值比较。