## 1 Introduction
[13] established a flexible job shop scheduling model considering transportation time, proposed a hybrid discrete particle swarm optimization algorithm for optimization, and introduced a competitive learning mechanism and random restart algorithm to avoid premature algorithms. [PERSON] et al. [14] proposed an improved NSGA-III algorithm, which introduced the reference-based niche selection mechanism to improve the diversity of the algorithm, and was used to solve the MOFJSP with the goal of minimizing the maximum completion time, total machine load, maximum machine load and machine energy consumption. [PERSON] et al. [15] used a mixed integer linear programming model to solve the green flowshop scheduling problem with the objective of minimizing the maximum completion time and total carbon emissions. [PERSON] et al. [16] proposed an improved non-dominated sorting genetic algorithm to solve the hybrid process shop scheduling problem under time-of-use and step tariff system with the optimization objective of minimizing the maximum completion time with respect to the total shop energy consumption. [PERSON] et al. [17] established a multi-objective mathematical model of flexible workshop with crane transportation constraints to minimize the maximum completion time and energy consumption, and optimized the model by combining a genetic algorithm with a firefly swarm optimization algorithm. However, with the deepening complexity of the mathematical model of MOFJSP, the traditional intelligent optimization algorithm often has some disadvantages in solving MOFJSP, such as slow running speed and fast algorithm convergence, and is easy to fall into local optimization in the iterative process. With the continuous updating of the new intelligent algorithm, it provides a new idea for solving the MOFISP problem more efficiently. The Wolf Pack Algorithm (WPA) is a pack intelligence optimization algorithm that simulates the division of labor and collaboration of wolves in nature to capture prey [18], with strong global search capability and computational robustness, and is used to solve problems such as multi-distribution center vehicle path [19], Traveling Salesman Problem (TSP) [20], and unmanned helicopter route path planning [21]. However, for workshop scheduling problems, there are still fewer WPA-related applications involved. In this paper, an improved Multi-Objective Wolf Pack Algorithm (MOWPA) is designed to solve the Multi-Objective Flexible job shop green scheduling mathematical model with the optimization objectives of minimizing the maximum completion time and minimum energy consumption, and generate the Pareto optimal solution set. The gray relational decision analysis method and Analytic Hierarchy Process (AHP) are introduced to select the Pareto solution set, and a new scheme is proposed to effectively solve the multi-objective flexible job shop problem. The contribution of this article can be summarized in three aspects: (1) In order to be more in line with actual production and processing, FJSP is extended according to the definition of FJSP, and a MOFJSP with transportation constraints is established. (2) An improved multi-objective wolf swarm algorithm is designed. The crossover and mutation operations of the genetic algorithm and pox crossover operations are introduced to improve the three intelligent behaviors of the wolf swarm algorithm. To comply with the multi-objective problem constraints, the WPA update method is designed and combined with non-dominated congestion ranking to solve the optimal Pareto solution set. (3) In order to facilitate the decision-maker to better select a scheduling scheme, this paper introduces the gray relational decision analysis method and analytic hierarchy process to calculate the Pareto solution set, and the decision-maker selects a scheduling scheme that is more consistent with the workshop processing according to the calculation results. The framework of the rest of the paper is as follows.