This article establishes a mathematical model for the flexible job-shop scheduling problem,aiming to minimize the maximum completion time of all workpieces under the constraints of processing sequence and processing time.A tri-population co-evolutionary algorithm is proposed to solve this model.Based on the three-way tournament method,the population is divided into superior,medium and inferior subpopulations,and corresponding search strategies are designed according to individual characteristics of each subpopulation.The superior subpopulation uses load balance and variable neighborhood descent local search of critical path to improve the solution accuracy and excavate better solutions.In the medium subpopulation,adaptive Jaya operation is used to tend to approach superiority and avoid inferiority in the early stage of evolution,and focus on maintenance of population diversity in the middle and late stages.Multi-variable crossover global search is adopted for inferior subpopulation,and crossover operators capable of generating viable individuals are designed for different gene strings.At the same time,individuals from other subpopulations are taken as potential mates for crossover to strengthen cooperative interaction among subpopulations.Extensive experimental results on standard test instances and production cases show that the proposed algorithm significantly outperforms representative algorithms in most cases.