## 4 Model Solution  
### Algorithm Construction  
The MEIFM problem formulated in the previous section is a fairly challenging problem. First, the integrated problem is a bi-level program, which is an NP-hard problem [29]. Second, it essentially entails combinatorial optimization, which contains a lot of 0-1 decision variables and several complicated nonlinear constraints, resulting in this model becoming highly non-convex. Third, as the three objectives considered in this paper have different attributes and units, it is difficult to use traditional approaches to obtain a reasonable solution that balances production efficiency and energy consumption. The traditional way of solving this kind of problem is to use Karush-Kuhn-Tucker (KKT) optimality conditions to replace the lower-level problem, which makes the bi-level programming model transform into a single-level model [30; 31]. However, this approach can only solve a linear and convex lower-level problem, which makes the approach hard to apply in real-world problems, such as non-linearity, discreteness, non-convexity etc. To conquer these problems, many researchers directly simulate the decision-making process of bi-level programming by using the hierarchical optimization algorithm. [PERSON] et al. [22] designed a bi-level multi-objective particle swarm optimization algorithm to solve the dynamic construction site layout and security planning problem. [PERSON] et al. [32] proposed a hierarchical hybrid particle swarm optimization and differential evolution algorithm to solve the pricing and lot-sizing decision problem. [PERSON] et al. [33] developed a bi-level GA to solve the mixed integer nonlinear bi-level programming for the product family problem. As a representative intelligence algorithm, the genetic algorithm simulates the evolution process of survival of the fittest and approaches the excellent results gradually. It has great value for solving bi-level programming problems due to its better global searching performance and robust performance. Therefore, this paper proposes an IMHGA to divide the optimization process of the integrated problem into upper and lower levels. The upper-level NSGA-II is used to determine the optimal scheduling scheme by minimizing the \(C_{\max}\) and \(TEC\), and the lower-level GA is employed to obtain the optimal layout scheme by minimizing the \(MHQ\). In the IMHGA, we design two improvement strategies to enhance the performance of the algorithm based on the characteristics of the MOBLP model. First, for the upper-level FJSSP, because its solution space is too large and the corresponding decision directly effects the optimization of the lower-level MRWLP, we need to find high-quality upper-level solutions as much as possible to guarantee the performance of the whole algorithm. However, it is difficult for the traditional NSGA-II algorithm to find an effective solution since most of the non-elitist solutions cannot fully participate in the genetic operation, which decreases the diversity of solutions and slows down the searching speed of the algorithm. To enhance the performance of the upper-level NSGA-II, we design the multi-parent improved precedence operation crossover (MIPOX) and multi-parent multipoint preservative crossover (MMPX) based on the multi-parent crossover method [34] for improving the quality of the Pareto solution set. The two crossovers not only satisfy the characteristics' preservation and feasibility between parents and their children, but also enhance the global searching ability of the algorithm and improve the diversity of the solution by combining multiple parent information. Second, for the lower-level MRWLP, its feedback directly impacts the evaluation of the upper-level FJSSP, so the convergence speed of the lower-level GA determines the convergence speed of the whole algorithm. Based on the concentration and diffusion strategy, once the scheduling scheme of the upper-level NSGA-II is determined, the lower-level GA will focus on finding the optimal layout scheme based on corresponding \(f_{lk}\).