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Scheduling for the flexible job shop scheduling problem is very important in the fields of production management and combinatorial optimization. However, in most real manufacturing environment, schedules are usually inevitable with the presence of a variety of unexpected disruptions. This paper proposes an efficient memetic algorithm to solve the flexible job shop scheduling problem with random job arrivals. Firstly, a periodic policy is presented to up date the problem condition and generate the rescheduling point. Secondly, the efficient memetic algorithm with a new local search procedure is proposed to optimize the problem in each rescheduling point. The new local search uses five kinds of neighborhood structures. Otherwise, the performance measures investigated respectively are: minimization of the makespan and minimization of the mean tardiness. Moreover, several experiments have been designed to test and evaluated the performance of the memetic algorithm. The experimental results show that the proposed algorithm is efficient with respect to bi-objectives and different due date tightness.