## 1 Introduction
### Contribution  
According to the above, an improved algorithm (IWOA) based on WOA was proposed to solve the green FJSP with AGV transportation. It is important to note that, like other meta-heuristic algorithms, WOA also has the disadvantages of easily falling into local optimum and premature convergence [36]. The global search ability of WOA has certain randomness and static clustering behavior, and its ability to jump out of the local optimum is limited, which leads to the tendency to fall into the local optimum in the process of solving the target problem. Furthermore, in the exploration stage of the WOA, the operation of learning from random individuals is blind, and there is no effective information exchange among groups, which affects the convergence speed of the algorithm. This problem is particularly prominent in large-scale complex optimization problems. To alleviate such problems, three techniques are used to improve the overall performance of the WOA. (1) A nonlinear convergence factor is introduced. The convergence decreases nonlinearly with the increase in the number of evolutionary iterations to ensure that the total group of whales moves with a large stride in the initial stage and a small stride in the later stage. It enhances the exploration ability of the algorithm and improves the convergence speed of the algorithm. (2) Nonlinear adaptive inertia weights were added to the algorithm to balance the local search and global search of the algorithm and avoid the algorithm falling into local optimization. (3) The screw position update model was improved to increase the diversity of the total population and retain more high-quality individuals to improve the solution quality. In addition, according to the characteristics of this model, a loss function based on fuzzy membership was constructed in order to obtain the optimal compromise solution of the multi-objective model. Considering the processing characteristics of the flexible workshop, that is, several operations can be processed on different machines, and the processing time, the processing energy consumption and processing quality of the same operation must be different for different machines. Therefore, it is not sufficient to take the completion time as the basis of shop scheduling without considering the energy consumption and processing quality of the shop. In short, on the premise of ensuring product quality and the stability of the production system, it is more practical to optimize the resource allocation strategy, improve the resource utilization rate, reduce the production energy consumption, and explore the green FJSP with the dual constraints of processing equipment and transportation AGV, which is closer to the real situation of modern workshops. The main contributions of this paper are as follows:  
(1) A multi-objective optimization scheduling model of a green flexible job shop was established to maximize the machining quality and minimize the makespan and energy consumption. In this paper, the energy consumption of the processing equipment and AGV scheduling were considered comprehensively. (2) An improved whale optimization algorithm (IWOA) was proposed and the fitness function of the algorithm constructed. (3) Based on fuzzy membership degree theory, the satisfaction function (loss function) was constructed to transform multiple objectives into a single objective. At the same time, several feasible scheduling schemes were provided to the decision-makers, so that the decision-makers could choose the optimal scheduling scheme according to the actual situation. In summary, the purpose of this research was to address the scheduling problem in a flexible workshop by establishing a multi-objective optimization model aimed at maximizing the processing quality while minimizing the makespan and workshop energy consumption. This study aimed to optimize resource allocation strategies, reduce energy consumption, and provide decision-makers with various feasible scheduling solutions to achieve an environmentally friendly production system.