## 1 Introduction
(2018) proposed a multi-robots cellular manufacturing system layout problem that can determine the positions of manufacturing components and task scheduling simultaneously, and they applied MOGA to solve the problem for minimizing the operation time, layout area, and manipulability. Although these studies validate that the ISLP can achieve better solutions than the independent optimization method, they still have several disadvantages, as follows:  
1. These studies cannot provide effective guidance for enterprises. Since most of these studies focus on the job shop scheduling problem (JSSP) and discrete workshop layout problem (DWLP), the flexible processing route of jobs and size of machines are neglected, which means that these studies cannot solve more realistic problems, such as the flexible job shop scheduling problem (FJSSP), single-row workshop layout problem (SRWLP), multi-row workshop layout problem (MRWLP), and so on;
2. The optimality of the layout scheme cannot be ensured. Because most studies of ISLP only consider scheduling objectives, the layout problem is simply appended to the scheduling problem as a constraint, which ignores the interaction between scheduling and layout planning. For the integrated model that only considers scheduling objectives, it is difficult to ensure the feasibility of the scheduling and layout schemes simultaneously. For example, if only the makespan is optimized, a scheduling scheme with lower makespan may be accompanied by an unreasonable layout scheme. The unreasonable layout scheme may result in frequent job delays and processing interruptions, which greatly offsets the economic advantage;
3. Only a few studies of ISLP consider the energy consumption indicator. If only optimizing the efficiency objectives, a solution with a higher production efficiency may also be a solution with higher energy consumption. The higher energy cost will have an adverse impact on the final profit of enterprises. Admittedly, we should seek a solution that balances energy consumption and production efficiency in solving the ISLP problem. To overcome these disadvantages, this paper chooses FJSSP and MRWLP, which are more suitable for the real manufacturing system as research objects, and focuses on the interaction between them. Then, the paper proposes a multi-objective energy-aware integration of FJSSP and MRWLP (MEIFM) problem. In the proposed MEIFM, we consider flexible processing routes of jobs and unequal-areamachines, as well as the interaction between FJSSP and MRWLP. The interaction is shown in Figure 1. The FJSSP is linked to the MRWLP by the material handling information and distance between machines. The FJSSP's decision guides the optimization of the layout scheme by material handling information, while the MRWLP's decision influences the performance of the scheduling scheme by distance between machines. Obviously, the MEIFM can be represented as a Leader-Follower or Stackelberg game, where the FJSSP acts as the leader and the MRWLP acts as the follower. Therefore, the MEIFM is a typical bi-level programming problem. As both scheduling and layout planning are NP-hard problems [20; 21], the MEIFM problem considering the flexible processing route of jobs and unequal-area machines becomes a more complicated problem. Additionally, it is concerned with balancing the production efficiency and energy consumption of the overall manufacturing system, which also makes the problem become more complex. Further, the bi-level programming problem also falls into the class of NP-hard problems [22]. As a result, developing an effective method to deal with the MEIFM problem is a challenge. To optimize the MEIFM problem, an improved multi-objective hierarchical genetic algorithm (IMHGA) is proposed. The proposed algorithm is designed based on the framework of GA, which is one of the most famous optimization algorithms and has been successfully applied in many bi-level programming problems [23; 24; 25; 26].