The static shortest path problem has been solved well. However, in reality, more networks are dynamic and stochastic. The states and costs of network arcs and nodes are not only uncertain but also correlated with each other, and the costs of the arcs and nodes are subject to a certain probability distribution. Therefore, it is more general to model the shortest path problem as a dynamic and stochastic optimization problem. In this paper, the dynamic and stochastic characteristics of network nodes and arcs and the correlation between the nodes and arcs are analyzed. The dynamic stochastic shortest path is determined. The dynamic stochastic optimization model of shortest path is provided, and a shortest path genetic algorithm is proposed to solve dynamic and stochastic shortest path problem. The effective and reasonable genetic operators are designed according to the topological characteristics of the network. The experimental results show that this algorithm can be used to effectively solve the dynamic stochastic shortest path problem. The proposed model and algorithm can be applied to the network flow optimization problem in transportation, communication networks, etc.