A re-entrant hybrid flowshop scheduling problem with lot streaming (RHFSP-LS) model was constructed in view of the difficulty of manual scheduling in array workshops to adapt to complex and variable production demands. An improved multi-objective migrating birds optimization algorithm was proposed for solving the model. A multi-objective migrating birds optimization algorithm based on non-dominated sorting, weighted sum, and external archive set was designed. The quality of the initial population was improved by using Logistic chaotic mapping and the NEH algorithm. A "sub-lot priority" + "batch priority" decoding strategy was proposed to enhance the algorithm’s solving capacity for special problems. A neighborhood search based on individual age was introduced to optimize the population’s neighborhood search direction. An escape mechanism combined with an external archive set was proposed to enhance the algorithm’s global search capability. The proposed strategies and algorithms were experimentally verified for the effectiveness and superiority in solving RHFSP-LS, ensuring an effective balance between the overall production cycle and the delivery deadlines of each process batch.