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Aiming at the flexible job shop scheduling problem of pipe heater based on AGV constraint, an improved sparrow search algorithm is proposed to solve the scheduling problem, aiming at minimizing the maximum completion time and the total load of the job shop. Establish a reasonable coding and decoding mode to represent the scheduling scheme; In order to solve the multi-objective optimization problem, Patero sorting is introduced. Considering the defects of sparrow search algorithm in solving discrete optimization problems, such as many invalid solutions and easy to fall into local optimum, this paper puts forward some improvement measures, such as introducing crossover and mutation operators, setting elite population and designing adaptive population scale factor. According to the standard example data and the actual workshop production data, the feasibility of the algorithm is verified. The results show that the improved algorithm can effectively solve a reasonable scheduling scheme. Compared with the original workshop production scheme, the production efficiency is increased by 19.6%, and the total load of the workshop is effectively reduced.