Based on the introduction of the concept of the 4th party logistics and the decision supporting system in its operation, the directed graph model with multi dimension weight was established for its optimization problem of how to select the route, the transportation method and the third party logistics provider concurrently. Genetic Algorithm is used to solve this directed graph model. An adaptive length-variant coding method is employed to represent the individual. The initial group is generated at random. After crossover and mutation are done, individuals are selected according to the rank they obtain when comparison is taken in the sense of fitness, of course randomly and elitism is applied. The results of experiments show that this Genetic algorithm can help to get the optimal solution to the directed graph model and solve the optimization problem in the operation of 4th party logistics.