Aiming at the problems such as poor search performance and low efficiency in existing multi-objective optimization methods, a multi-objective optimization method based on grey synthetic incidence analysis is proposed. In the proposed multi-objective optimization method, a high quality reference sequence is firstly constructed by a single objective optimization algorithm, the grey synthetic incidence degree between the reference sequence and the objective function value sequence of the optimized solution is calculated, and then the dominance relationship of different solutions based on grey synthetic incidence degree is defined. Finally, the grey synthetic incidence degree is used as the fitness value of the multi-objective optimization algorithm. The multi-objective flow shop scheduling problem with sequence-dependent setup times is taken as the application object, and a multi-objective optimization model including the objectives of total production cost, makespan, mean flow time and machine mean idle time is developed. A multi-objective fireworks algorithm based on grey synthetic incidence analysis is proposed to solve the proposed multi-objective optimization model. The simulation experiment shows that the performance of the proposed multi-objective fireworks algorithm is better than these fireworks algorithms based on the different multi-objective optimization methods and two popular multi-objective algorithms, thus the feasibility and effectiveness of the proposed multi-objective optimization method are verified.