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In order to improve the quality of solution obtained by multi-objective evolutionary algorithm, researchers have done a lot of research. The traditional multi-objective evolutionary algorithm based on Pareto dominance relationship has certain limitations. This paper combined different domination relations with NSGA-II(Non-dominated Sorting Genetic Algorithm)to solve the multi-objective optimization problem of flexible job shop scheduling carried by a single robot, and compared and analyzed the advantages and disadvantages of different methods in solving high-dimensional multi-objective optimization problem through experiments. This paper takes NSGA-II as the framework, combines Lorenz dominant relation and CDAS(Control Dominance Area of Solutions)dominant relation, and the traditional NSGA-II based on Pareto dominant relation studies the same optimal scheduling problem, and finds that the optimization algorithm based on Lorenz dominant relation and CDAS dominant relation has better effect than that based on the traditional Pareto dominant relation.