Obtaining of the shortest path set plays an important role in traffic network calculation n .However, most of existing algorithms do not consider the delay in the intersection and are not suitable for finding path set , and the effect of them is not ideal . Decision variables are the location of park and ride facilities, train stations and the frequency of public transport lines. For a case study the Pareto set is estimated by the Non-dominated Sorting Genetic Algorithm .By considering above problems , the encoding method of genetic algorithm(GA)is analyzed and encoding space and solution space are compared .After that , the encoding method based on path is adopted and a mutation operator is designed considering the intersection delay to overcome the complexity .At last , the designed GA and the GA of priority based encoding method are used in a group of networks ,which are generated by using a random network generator , and the calculation results of them are also analyzed .The result verifies the efficiency of the designed GA .