Joint scheduling optimisation method for the machining and heat-treatment of hydraulic cylinders based on improved multi-objective migrating birds optimisation

For the hydraulic cylinder parts manufacturing shop scheduling problem (HCPMS), which integrates a parallel batch processor hybrid flow shop scheduling problem with the flexible job shop scheduling problem, this paper establishes a multi -objective scheduling model with makespan, total energy consumption, and total machine workload as the optimisation objectives, and proposes an improved multi -objective migrating birds optimisation (IMOMBO) algorithm to solve the problem. First, considering the characteristics of the combination of singlepiece and batch processing in the workshop, a double -layer coding rule based on the operation and processing equipment is proposed, and the corresponding decoding rule is designed according to whether the workpiece requires quenching and tempering. Second, a multi -population co -evolution mechanism is developed to enhance the diversity of solutions by conducting different evolutionary strategies. Additionally, six neighborhood structures are introduced to perform local searches for the leader and follower birds, thereby improving the quality of the solutions. Finally, the effectiveness of the IMOMBO algorithm is demonstrated by comparing its results with those of four other algorithms through comparative experiments and a practical case.