Cross Entropy Chance Distribution Model of Uncertain Random Shortest Path Problem

Abstract

The shortest path problem (SPP) is one of the most typical and basic optimization problems in network theory for decades, and it covers a series of practical application problems, such as urban planning, logistics transportation, engineering and power grid strain analysis, etc. The circumstance where the weight of arcs in a network contains both randomness and uncertainty is considered, and the case of the weights of arcs with uncertain random variables is focused on in this paper. Here, we introduced a new model of the SPP which is based on the new definition of uncertain random variables cross entropy, and the newly established model can be used to find the path with the closest chance distribution to the ideal SP. The efficiency of this model is also evaluated in the final part.