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Focusing on the problems of uncertainty and carbon emissions in the manufacturing process, this paper studies the low-carbon-emission scheduling optimization problem. Firstly, the variations in workpiece processing time and delivery date are selected as the uncertainty factors. A low-carbon-emission scheduling model for uncertain job shops is constructed with the optimization objectives of the time index, carbon emission index, and robustness index. Secondly, an improved third-generation non-dominated sorting genetic algorithm (NSGA-III) is proposed. Based on the original NSGA-III algorithm, this algorithm introduces the state transition algorithm to perform state transformation, neighborhood sampling, selection update, and alternate rotation operations on the parent population, generating new candidate solutions. Finally, the scheduling model and the improved algorithm are applied to a workshop example. Through case study computation and result analysis, the feasibility and effectiveness of the model and algorithm in addressing the low-carbon-emission job shop scheduling problem under uncertainty are further verified.

The rotation error is the most important quality characteristic index of a rotate vector (RV) reducer, and it is difficult to accurately optimize the design of a RV reducer, such as the Taguchi type, due to the many factors affecting the rotation error and the serious coupling effect among the factors. This paper analyzes the RV reducer rotation error and each factor based on the deep Gaussian processes (DeepGP) model and Sobol sensitivity analysis(SA) method. Firstly, using the optimal Latin hypercube sampling (OLHS) approach and the DeepGP model, a high-precision regression prediction model of the rotation error and each affecting factor was created. On the basis of the prediction model, the Sobol method was used to conduct a global SA of the factors influencing the rotation error and to compare the coupling relationship between the factors. The results show that the OLHS method and the DeepGP model are suitable for predicting the rotation error in this paper, and the accuracy of the prediction model constructed based on both of them is as high as 95%. The rotation error mainly depends on the influencing factors in the second stage cycloidal pinwheel drive part. The primary involute planetary part and planetary output carrier’s rotation error factors have little effect. The coupling effects between the matching clearance between the pin gear and needle gear hole (δJ) and the circular position error of the needle gear hole (δt) is noticeably stronger.