Abstract: A perturbation algorithm with minimum edges is proposed to solve the problem of how to make a specific target path become the shortest path with the minimum cost on the premise of disturbing the minimum edges. The algorithm is based on the shortest path perturbation model with the fewest edges. By introducing the perturbation upper limit constraint of each edge weight, the biobjective mixed integer programming problem of minimizing the number of perturbation edges and minimizing the total cost of perturbation is established. Thus, the shortest path between the nodes of the control network is realized. Compared with the previous minimum cost perturbation algorithm, this method reduces the complexity of perturbation and the risk of disturbance network being detected. Experiments show that the optimal solution reduces the number of perturbed edges by about 27% and has better performance.