## 1 Introduction
### Literature Review
[30] considered a green job-shop scheduling problem and constructed a planning model aimed at minimizing the sum of energy consumption cost and completion time cost of the workshop, and designed an optimized discrete whale to solve the model. [PERSON] et al. [31] developed an optimization model aiming at minimizing the AGV energy consumption and production cost, and proposed a nonlinear mixed integer programming genetic algorithm. [PERSON] et al. [32] established a green shop scheduling optimization model aimed at minimizing the total energy consumption and proposed an improved African Buffalo optimization algorithm to solve this problem. In order to balance production and green and sustainable development, [PERSON] et al. [33] constructed a multi-objective flexible job-shop scheduling model with processing time, energy consumption, and noise minimization as the objectives under the dual resource constraints of human and machine, and developed a hybrid discrete multi-objective imperial competitive algorithm based on the model. [PERSON] et al. [34] proposed a new enhanced meme algorithm to solve a job-shop scheduling problem with dual objectives, namely, minimum machine energy consumption and minimum makespan. [PERSON] et al. [35] explored the energy consumption of AGVs in manufacturing environments and investigated the AGV energy-efficient scheduling problem with customer satisfaction in flexible manufacturing systems. The whale optimization algorithm (WOA) is a new meta-heuristic algorithm proposed by [PERSON] et al. in 2016 [36]. It has the advantages of a simple search strategy, few parameters, and strong search ability. Compared with other classical algorithms (genetic, particle swarm optimization, ant colony, etc. ), the main uniqueness of the WOA algorithm is that it can maintain a good exploration and development relationship by self-adjusting some parameters in the iterative process, and it has been widely used in solving a variety of optimization problems [37; 38; 39; 40]. In terms of shop scheduling, [PERSON] et al. [41] proposed a new and improved whale optimization algorithm to solve the scheduling scheme of a flexible shop scheduling problem. They improved the convergence factor of the whale algorithm and introduced the inertia weight. [PERSON] et al. [42] introduced a nonlinear convergence factor and mutation operation of scheduling rules on the basis of a standard WOA algorithm. [PERSON] et al. [43] proposed a hybrid whale swarm optimization algorithm (WOA-LFDE) based on Levy flight to solve the problem of job-shop scheduling optimization, and improved the search ability and convergence speed of the algorithm by changing the search strategy and flight mode. To sum up, existing studies have made many achievements in the model construction and algorithm solving of a FJSP. The summary is as follows:  
(1) In a FJSP that adopts an AGV for material transportation, few existing studies have put forward restrictions on the number of AGVs. In addition, the path optimization of processing equipment allocation and AGV scheduling scheme is considered more, and the objective function constructed is mostly a single objective programming model, that is, the makespan is minimum, without considering the shop energy consumption and processing quality. (2) In the existing green FJSP, scholars take the completion time and energy consumption of processing equipment into consideration when modeling, but there are few studies on the joint scheduling of processing equipment and AGVs from the perspective of green scheduling. Therefore, the energy consumption in the existing green FJSP only considers the energy consumption of processing equipment, while ignoring the energy consumption of AGV scheduling. (3) In the optimization algorithm of the FJSP solution, many improved algorithms based on genetic algorithm, tabu search algorithm, ant colony algorithm, and other classical intelligent algorithms have been applied, but the local search performance and convergence speed of the above algorithms still need to be further improved.