# Research on Low-Carbon-Emission Scheduling of Workshop under Uncertainty
## 1 Introduction
According to the reviewed literature, most low-carbon optimization scheduling studies focus on single machines or flow shops. However, the workshop is a complex, flexible job shop that is full of complexity, uncertainty, multiple constraints, and a multi-objective nature. Further research needs to be carried out on complex flexible workshops. [PERSON] et al. [17] used the EDA method (understanding the estimation of distribution algorithm) to solve the stochastic flexible job shop scheduling problem with a min-max regret version and processing time uncertainty. To solve the flexible job shop scheduling problem, [PERSON] et al. [18] designed a hybrid Pareto algorithm based on fuzzy logic to minimize the maximum completion time and the total machine load. [PERSON] et al. [19] developed a neighborhood search algorithm based on a multi-objective group to solve the fuzzy flexible job shop scheduling problem by minimizing the maximum fuzzy completion time and machine load. [PERSON] et al. [20] proposed an overall DT-enabled real-time scheduling (DTE-RS) framework for complex product shop-floors to effectively reduce adverse impacts of the dynamic disturbances and minimize the makespan based on a global twin. [PERSON] et al. [21] established a job shop scheduling model with total delay time and carbon emissions as objective functions and proposed a new multi-objective imperialist competition algorithm to solve the problem. [PERSON] et al. [22] extended the flow shop scheduling problem to optimize low carbon emissions and variable processing parameters. They proposed two scheduling methods for specific problems to describe the scheduling problem. [PERSON] and [PERSON] [23] proposed a bi-population-based discrete bat algorithm to research the low-carbon job shop scheduling problem. To minimize the negative impact of uncertain factors on production, ensure the stability of the production system, and realize low-carbon and efficient operation of the manufacturing system, based on an in-depth discussion of the uncertain factors in the job shop, combined with a relevant literature search, this paper selects two typical uncertain factors (uncertain processing time and uncertain delivery date) as the uncertain factors in the production process. The corresponding mathematical tools are used to describe the uncertain factors, and the uncertainty-oriented low-carbon scheduling model of the job shop is constructed. Considering the lack of convergence in the genetic algorithm [24], this paper proposes an improved NSGA-III based on the state transition algorithm (NSGA-IIIST), which is proposed as an extension of the NSGA-III by introducing the state transition algorithm and enhancing the initial clustering operator, while maintaining the properties of the NSGA-III. The optimization of the manufacturing system's low-carbon, efficient, and orderly operation is realized by applying the model and algorithm to the actual production scenario. The main contributions of the paper are as follows:  
1. A multi-objective low-carbon-emission scheduling model for workshops under uncertainty is established, which optimizes green indexes such as carbon emissions and economic indexes such as the robustness index and time-based index, using the processing time and order delivery time as uncertainty. By optimizing the workshop model, the manufacturing process can achieve low-carbon, economic, and efficiency goals. 2. An improved NSGA-III-ST algorithm is proposed. The algorithm is a hybrid of the NSGA-III and the state transition algorithm. The test also validates the feasibility and validity. Our work has critical academic significance and engineering value for multi-objective optimization problems in the context of low carbon goals.