Abstract: A mathematical model for a locomotive diagram of a train diagram with paired and non-paired trains was presented,and the optimized schedule was obtained with a genetic algorithm.The abilities of local search,convergence and optimization were raised with a two-point crossover operator and a knowledge-based mutation operator.The proposed method was tested over an actual problem of train diagram for a district on a railway line.The results show that the total time of locomotive operation and the required number of locomotives are reduced by about 5.7% and 7.7%,respectively.Another result shows that the proposed method reduces total time of locomotive operation compared with the method presented and for the same data taken in the same paper.