Model and Algorithm for Continuous Time-Varying Shortest Path Problem

Abstract

Shortest path problem is a common problem in traffic areas. In an actual traffic network, arc costs are usually time-varying functions, under such condition, the issue how to find a shortest path is called as time-varying shortest path problem, on which there are a few research so far, and these research are all aiming at the following situations: arc costs are discrete time-varying functions, piecewise functions, or probability distribution functions. However, arc costs are often continuous time-varying, and there is hardly any research on shortest path problem under this condition. Therefore, we establish a nonlinear programming model and design a corresponding dynamic Dijkstra algorithm on continuous time-varying path problem, whose correctness and effectiveness are verified through a case study.