With the development of economy, robotic of economy, robotic cells have greatly improved the production efficiency and quality of the manufacturing industry. Compared with that of the traditional flexible manufacturing cells, the scheduling problem of shops with robot handling also involves material handling. As a result, the production scheduling problem is becoming increasingly complex. In view of the lack of dominance of the Pareto dominance relation in high-dimensional multi-objective optimization, the Lorenz domination and CDAS domination are combined, respectively, with the non-dominated sorting genetic algorithm-III (NSGA-III) algorithm in this study and applied for the first time to the high-dimensional multi-objective scheduling of shops with robotic cells. Considering the complexity of modern production processes, this study proposes to optimize multiple objectives, such as maximum completion time, total processing energy consumption, delivery lead time, delivery delay time, and total production cost, at the same time to determine the operating state and handling sequence of the robot and improve production efficiency. Experiments show that on the abovementioned production scheduling problem, the NSGA-III algorithm based on Lorenz domination or CDAS domination performs better than the traditional NSGA-III algorithm in the solution convergence and uniformity.