A Nonlinear Mixed Integer Programming Method to Find the Reliable Shortest Path in a Stochastic Network

摘要

A reliable shortest path problem is focused on finding a reliable a priori shortest path to maximize the probability of travelers arriving at their destination within a given travel time budget in a stochastic network. The mathematical model based on nonlinear mixed integer programming is established to analyze the problem of finding the reliable shortest path in a stochastic traffic network. A penalty method is developed to solve the nonlinear mixed integer programming problem by transforming the proposed problem to an unconstrained nonlinear programming problem through penalty function. Numerical results are provided using a small network and show the validity and feasibility of the proposed method.