Abstract: Aiming at the vehicle scheduling problem with time window,a hybrid quantum evolutionary algorithm with immune operator was put forward．The algorithm improves quantum rotating gate,making individual in evolutionary process close to the global optimum position,so as to avoid prematurity and to maintain the diversity of the population．In the iteration process,an immune operator is introduced,and excellent genes fragment is extracted as vaccine which was vaccinated to the other individuals in the population,as to prevent the algorithm retrogression．Finally,the experimental simulations of the standard instances show that the proposed method can not only effectively solve the problem,but also significantly speed up the convergence.

Key words: Vehicle scheduling problem,Quantum rotating gate,Immune operator,Quantum evolutionary algorithm