Reconstruction Layout Optimization of Multivariety and Small Batch Workshop in Aerospace Industry

To cope with the problems of frequent mold changes, long production cycles and serious logistics crossings in workshop of aerospace enterprise. First, a manufacturing cell layout planning method based on the feature bit code domain method and K-Means++ is proposed to realize the accurate division of manufacturing cells. Then, a multiobjective optimization method of dynamic reconstruction layout based on improved fruit fly optimization algorithm (IFOA) is proposed to solve the reconstruction layout optimization of the production workshop problem with the optimization objectives of logistics cost, reconstruction cost, loss cost, and cell integrated area. Finally, plant simulation software is applied to simulate the workshop layout before and after optimization. The simulation results show that the logistics cost of the workshop cell layout after optimization is reduced by 8.7%, the utilization rate of the workshop area is improved by 5.2%, and the value-added rate of products is increased by 6.6%, which verifies the effectiveness and feasibility of the proposed model and method.


Introduction
Te production workshop of an aerospace enterprise is a typical multivariety and small batch discrete production workshop, and the products are characterized by many varieties, small batches, many parts, complex production processes, and coexistence of production and development. Most of the existing production workshops of aerospace enterprises still adopt the traditional cluster layout, which makes it hard to meet the continuously increasing variety of aerospace product production in recent years. According to statistics, the logistics cost and production cost wastage caused by an unreasonable workshop layout reaches 20%-50% of the total cost of production system, and the workshop production cost can be efectively reduced by 10%-30% through reasonable planning of workshop layout [1]. Terefore, an efective optimizing method of production workshop layout in the aerospace enterprise is of great practical signifcance to reduce the comprehensive costs of workshops as well as improve the value-added rate of products.
Te multivariety and small batch facility layout problem is a high-dimensional and nonlinear NP-hard problem [2]. Although the existing cell layout in an aerospace enterprise workshop can carry out the normal production of multivariety and small batch products, the cell formation is subjective and poor in accuracy, while the logistics within the cell are extremely chaotic and costly. Tus, it is still a difcult problem to reasonably construct the manufacturing cell and plan the production logistics within the cell. In recent years, a lot of work has been carried out on cell formation and workshop layout from the perspective of modeling optimization.
In a static environment, scholars at home and abroad have done a lot of research studies [3][4][5][6][7][8][9][10][11][12][13][14]. Sabrina and Menouar [3] proposed a graph-theoretic model based on group technology principles and developed two B&B algorithms to solve the manufacturing cell formation problem. Liu et al. [4] constructed a timed Petri net model based on the functions and connections of each production cell for a discrete production plant and applied FlexSim for simulation optimization, efectively reducing the cross-detour routes of the plant and the idle rate of the equipment, and improved the productivity of the plant. Wu et al. [5] proposed an improved ant colony optimization algorithm for the large-scale factory layout problem, and the safety, geographic, and environmental constraints are considered in the optimization process to achieve the spatial allocation of the factory layout. Liu et al. [12] used a new heuristic algorithm to obtain Pareto-optimal solutions to the problem and proposed a heuristic layout updating strategy and a niche technology to solve the unequal area facility layout problem. Ren et al. [14] developed a methodology for the reconfgurable modular facilities layout problem with alternative process routings, and an integrated mathematical model is proposed to improve production fexibility and minimize material handling costs.
Many research results have been published by domestic and overseas scholars on dynamic layout optimization problems [15][16][17][18][19][20][21][22][23][24][25]. Wei et al. [15] developed a layout model for the reconstruction manufacturing system and applied the chaos genetic algorithm to solve the dynamic facility layout problem. Kheirkhah and Bidgoli [16] proposed an improved simulated annealing algorithm based on graph theory for solving the dynamic facility layout problem by transforming it into the shortest path problem based on practical constraints. Te validity of the model and the solution method is verifed by numerical experiments. Liu et al. [24] described a model based on the dynamic facility layout problem and combined the Wang-Landau sampling algorithm and some heuristic strategies to solve the unequal area dynamic facility layout problem. Xiao et al. [25] proposed a hybrid robust optimization model for the unequal area dynamic facility layout problem considering the location of pick-up and drop-of points to solve the product demand uncertainty problem. Furthermore, an improved particle swarm optimization algorithm is developed to solve the proposed model. A summary of the research literature on workshop layout issues is shown in Figure 1.
As mentioned previously, extensive results have been achieved in workshop cell construction and layout optimization. However, there are some limitations in the division of manufacturing cells, specifc layout of equipment within the cell, and reasonable evaluation of layout schemes in the workshop of aerospace enterprises. At present, most of the research studies on product family construction revolve around grouping techniques, which only start from the product's properties and ignore the actual situation of processing equipment, resulting in an unsatisfactory division of manufacturing cells, and the processing equipment used for the same product family cannot be concentrated in the same cell. After the product family is constructed, it still needs to be artifcially adjusted to make the processing equipment concentrated in one manufacturing cell, which cannot guarantee the objectivity of manufacturing cell division. Moreover, the reconstruction layout within the cell can be summarized as a multiobjective dynamic discrete combinatorial optimization problem, for which the largescale NP complete exact solution cannot be obtained in a limited and reasonable time. Tis leads to slow convergence of the existing algorithms in solving problems and unsatisfactory multiobjective solutions, which cannot cope with the dynamic changes of the reconstruction layout.
Te main contributions of this study can be concluded as follows. (1) A reconstruction workshop layout model with the objectives of minimum logistics costs, reconstruction costs, loss costs, and integrated cell area for multivariety and small batch aerospace enterprise is established. (2) A novel IFOA is proposed to obtain the optimal reconstruction layout plan of aerospace enterprise workshops. (3) Te plant simulation is employed to assess the efectiveness of reconstruction layout plans before and after optimization. Te rest of this study is organized as follows. Te layout planning method is introduced in Section 2. In Section 3, the modeling process of the dynamic reconstruction layout optimization problem is presented. Section 4 performs a novel IFOA, and a case study is provided to verify the efectiveness of the method in Section 5. In Section 6, the computer simulation and analysis are conducted. Section 7 summarizes the fndings and future works.

Layout Planning Method
To address the problems of frequent product mold changes and serious logistics crossovers in the production workshops of aerospace enterprises, product families are constructed to reduce the number of product tooling switches and production preparation time, and manufacturing cells are constructed to centralize material fow within the cells to reduce logistics chaos and handling waste. Parts can be categorized into design families, machining families, numerical control families, and management families according to their similar characteristics, among which machining families are applied to grouping processing and facility layout of parts [26]. Existing studies mainly apply grouping techniques to construct product families; however, due to only considering the process similarity and ignoring the product process routes, equipment used for processing the same family of products cannot be concentrated in the same cell, and the product families still need to be artifcially adjusted. Terefore, we apply the feature bit code domain method to construct the product design family from the attributes of parts, make preliminary clustering of products, and then apply the K-Means++ clustering algorithm combined with the productequipment matrix to accurately cluster products to construct the product processing family and divide manufacturing cells.
Te feature bit method encodes the parts by selecting a specifc feature bit in the coding system to avoid encoding all the bits in the part coding system. Te code domain method is based on the code bit of the part classifcation coding system, increasing the domain value of the code bit and allowing parts with diferent coding but similar partial characteristics to be classifed into one class. Te hybrid method of feature bit and code domain increases the number of components that can be grouped within the group. With the classifcation of the part features, the requirements for each feature bit are appropriately relaxed, allowing more parts with similar structures and features to be grouped into a product family. Te coding process of this hybrid method is shown in Figure 2.

Computational Intelligence and Neuroscience
In this way, the K-means++ algorithm and elbow method are applied to overcome the shortcomings of the traditional K-means algorithm. Te K-means++ algorithm is based on the traditional K-means algorithm, which makes improvements to the initial clustering center selection; assuming that n manufacturing cell centers have been selected (0 < n < K), then when selecting the frst n + 1 manufacturing cell centers, the more distant points from the current n manufacturing cell center have a higher probability to be selected as the frst n + 1 manufacturing cell centers. Additionally, it overcomes the efect of random selection of the initial clustering centers of the traditional K-means algorithm and efectively improves the clarity and efciency of manufacturing cell classifcation [27]. Te specifc processes  Computational Intelligence and Neuroscience of the K-means++ algorithm for classifying the manufacturing cells of complex aerospace components are summarized as follows: Input: product-equipment matrix X � x 1 , x 2 , · · · , x n and number of manufacturing cells K Output: K manufacturing cells both product processing families C j and j � 1, 2, · · · , n Step 1: we randomly select a sample of points from the product-equipment matrix as the cluster center of the current manufacturing cell m r .
Step 2: we calculate the shortest distance between each sample and the center of the current manufacturing cell D(x) � argmin‖x i − m r ‖ 2 2 , where ‖x i − m r ‖ 2 2 represents the L2-norm of vectors D(x), that is, the Euclidean distance. On this basis, the probability of each sample point being selected as the center of the next manufacturing cell is calculated: D(x) 2 / n i�1 D(x i ) 2 . We select the next manufacturing cell center according to the roulette method.
Step 3: we repeat step 2 until K manufacturing cell centers are selected.
Step 4: for each sample in the dataset x i , we calculate its distance to the center of the K manufacturing cells and classify it in the manufacturing cell with the smallest distance.
Step 5: for each manufacturing cell C j , we recalculate its manufacturing cell center m r � (1/|m r |) x i ∈m r x i .
Step 6: we repeat steps 4 and 5 until the position of the center of all manufacturing cells no longer produces a change.
To determine the number of manufacturing cells K, the elbow method is selected to determine the cluster number K based on the construction of product design families. Tis method calculates the sum of the squared errors (SSE) of the dataset when constructing diferent manufacturing cells for the current workshop product and equipment situation as shown in equation (1), to judge the merit of the clustering efect. When K is less than the true clustering number, an increase in K will substantially increase the degree of aggregation of each cluster, so the decrease in SSE will be large, while when K reaches the true clustering number, the degree of aggregation obtained by increasing K again will rapidly become smaller [28], so the value of K corresponding to this infection point will be called the true clustering number: where C j , x i , m r , and SSE refer to the group j, the sample points in C j , the nature heart of C j , and the clustering error of all samples and refect the strength of the clustering efect, respectively.

Model Framework
Te model framework is explained in the following sections.

Problem Description.
In the multivariety and small batch workshop of the aerospace industry, due to the special characteristics of some movable equipment in aerospace enterprises and the characteristics of multivariety switching of aerospace products, the dynamic reconstruction layout of equipment in the manufacturing cell of the production workshop is needed to cope with the real-time changes caused by the multiproduct switching of typical aerospace complex components on the workshop and to solve the problem of whether the equipment position needs to be adjusted to reconstruct the current layout to ensure the efciency of the system when the products are switched. Te layout of equipment in the cell mostly uses linear layout or U-shaped layout in actual production as shown in Figure 3. In a cell for multistation continuous operation, compared with the pipeline layout using U-shaped layout, workers move shorter distances, and higher productivity can facilitate the training of multiability workers. Meanwhile, the infuence of equipment orientation on the cell area should be considered when designing the cell layout. Terefore, a U-shaped cell reconstruction layout model is established to achieve the minimum of cell logistics cost, reconstruction cost, loss cost, and cell comprehensive area within actual constraints. A schematic diagram of the equipment layout within its workshop manufacturing cell is drawn as shown in Figure 4.
Furthermore, to simplify the problem at hand, we suppose the following. (1) Since equipment used in the workshop is mostly machining centers, we suppose that each piece of equipment is rectangular. (2) Each piece of equipment is arranged in branches in the cell, each row is parallel to the horizontal axis, and the center point of equipment in the same row is located on a horizontal line.
(3) Since the center of most equipment coincides with the center of mass, it is assumed that the distance between equipment is the absolute value of the diference between the transverse coordinates of the center of mass and that the  Computational Intelligence and Neuroscience logistics are carried out from the center of mass. (4) Te material fow between each piece of equipment is constant within the current stage and changes in diferent stages.

Objective Function.
Te objective function of the model framework is explained in the following sections.

Material Transport
Cost u 1 . Te calculation of the material transport cost in the cell is the sum of the transport cost per unit distance of the product in each stage, transport times, transport batch, and transport distance: where X tik and X tjl decision variables are used to represent the movement of equipment at diferent stages.

Equipment Reconstruction
Cost u 2 . Te cost of equipment reconstruction mainly involved equipment moving cost and equipment resetting cost which can be calculated by

Loss Cost during Equipment Reconstruction u 3 .
In practice, to guarantee the continuity of production, all equipment are shut down during the equipment reconstruction, so the loss cost is not the proft loss of single reconstruction equipment, but the proft loss of all equipment in the cell during the reconstruction:

Comprehensive Cell Area S.
To ensure the orderly and safe fow of products between the cells and leave enough space for subsequent track planning, the minimum spacing between cells is required, and equipment in the cell should meet the compactness principle as far as possible. Terefore, the infuence of layout dynamics and equipment layout direction on area is considered: Finally, a multiobjective optimization model of manufacturing cell reconstruction layout for aerospace enterprises is established as follows.
Te objective function is  Computational Intelligence and Neuroscience Constraints are Equation (7) indicates that the sum of equipment reconstruction cost and loss cost during reconstruction must be less than the budgeted cost. Equation (8) ensures that, at each stage, each location can only accommodate one piece of equipment. Equation (9) depicts that each piece of equipment can only be placed in one position at each stage. Equation (10) guarantees that equipment does not overlap or interfere in the horizontal direction. Equation (11) constrains equipment, so it does not overlap or interfere in the vertical direction.
Note that the dynamic nature of the model is refected in the change of stage t. As the production workshop of the aerospace enterprise is batch production, the logistics amount between each piece of equipment is constant in the current stage, and the production of the next product is started only after the current product batch is all produced, so the production process of the frst product of the order is regarded as the frst stage t 1 in a manufacturing cell, and when the frst product is all produced, it is judged whether it is necessary to adjust the current. If no reconstruction is required, the current layout is retained to enter stage t 2 . If reconstruction is required, the product production in stage t 2 starts with the reconstructed layout.

Proposed Optimization Algorithms
Te proposed optimization algorithms are explained in the following sections.

Algorithm
Design. U-shape cell reconstruction layout problem has nonlinear and NP-hard characteristics. Te complexity of the solution is mainly manifested as the complexity of reconstruction dynamic layout and multiobjective solution which the computational complexity is mainly refected in the scale of the layout problem. Swarm intelligence optimization algorithms show high performance for solving this problem [7,12,13,[29][30][31]. However, for solving multiobjective dynamic facility layout problem, due to the limitation of equipment location coding, the traditional algorithms such as genetic algorithm and ant colony algorithm may converge slowly, which cannot adapt to the real-time dynamic change of reconstruction layout.
Te fruit fy optimization algorithm proposed by Pan is wildly applied to solve combinatorial optimization problems in recent years, as a result of its strong coding adaptability and fast convergence speed [32]. For solving multiobjective optimization problems, existing studies only combine linear weighting to transform multiobjective problems into single-objective problems, which makes the weight coefcients highly subjective. Terefore, based on the FOA, we introduce the cross-mutation strategy, fast nondominated sorting mechanism, and a random search mechanism based on visual search to improve the stability of the solutions. In this way, the problem of multiobjective dynamic workshop layout is solved; the U-shaped cell of the specifc layout of equipment is obtained. Te FOA pseudocode is shown in Figure 5, and the fowchart of IFOA is shown in Figure 6.

Encoding Method.
To satisfy the workshop restrictions and actual needs of the enterprise, equipment in the manufacturing cell in this study follows the U-shaped counterclockwise arrangement principle, which is convenient for workers to operate and can efectively avoid the intersection of logistics. For this reason, for U-shaped manufacturing cell, equipment encoding adopts a mixed encoding method of integer and binary encodings, where the equipment position adopts an integer method, the order is from left to right at the bottom layer, the median is the middle layer, and the top layer is counterclockwise from right to left. In the coding sequence, the center of equipment coincides with the center of the location. For example, one of the nine pieces of equipment in the reconstruction equipment layout is coded as [1][2][3][4][5][6][7][8][9] as shown in Figure 7. If the number of pieces of equipment is even, a piece of virtual equipment is introduced. Te equipment layout direction part adopts (0, 1) binary coding mode, and 0 means that the length of equipment is parallel to the horizontal direction of the cell, while 1 means that the length of equipment is perpendicular to the horizontal direction of the cell. For nine pieces of equipment, an encoding example of their chromosomes is shown in Figure 8. Te chromosome adopts this encoding method to directly obtain the specifc position of each equipment without decoding.

Defne the Olfactory Radius.
Randomly, we generate P initial populations. Te defnition of olfactory radius is the exact search step length. In this algorithm, it is expressed as the number of equipment exchanges. Te defnition OR � 2 means that two pairs of equipment bits are randomly selected for exchange. Since the code needs to be a nonrepetitive number, the counterpoint crossing method is adopted.

Olfactory Search and Fast Nondominated Sorting.
Fruit fy gradually approaches food through smell, and substituting new individuals into equation (12) food concentration determination function to calculate food concentration (smell), where s represents the individual fruit fy, the equipment sequence, and F(s) represents the objective function value, which is the minimum logistics cost at the current stage. Te greedy method is used to search for a better equipment layout. Te olfactory search process is shown in Figure 9: Multiobjective sorting of food concentration values is that, between the cell reconstruction cost and cell comprehensive area, the lower the level, the higher the ranking, and the higher the crowding degree. We select the top fruit fy as the current optimal fruit fy position for subsequent visual search and random search.

Visual Search and Random Search.
Fruit fy approaches food quickly by visual, increases the search step, and sets VR � 3; that is, three consecutive device positions are randomly selected for exchange or variation. Te induction probability p is introduced in this process. After nondominated sorting, the frst p% individuals perform a visual search, and the remaining individuals perform a random search. For the visual search, fruit fies approach food quickly through vision and randomly select three consecutive machine tools positions for the entire exchange as shown in Figure 10. In the random search stage, fruit fies fy randomly according to the visual step length to ensure the diversity of the population and prevent it fall into local optimum, that is, randomly select three consecutive machine tools positions for random rearrangement as shown in Figure 11.

Case Study
Tere are many problems in the layout of an enterprise; the more signifcant ones can be concluded as follows: the average daily logistics volume between computerised numerical control (CNC) boring and milling machining center and electrical discharge machining (EDM) in the clamping area is as high as 25,723 kg, the highest in all manufacturing cell pairs, but the two stations are not close to each other, there is other equipment in between, and the transportation route is as long as eleven meters. Te logistics route between the three-axis CNC vertical milling and four-axis boring and milling machining center and the horizontal milling and EDM equipment crosses, and the automated-guided vehicle (AGV) often stops on the route. To cope with the above problems, the layout optimization of complex component production workshop is carried out to verify the feasibility and efectiveness of the proposed method in this study. Te aerospace workshop adopts the traditional cluster layout, which consists of twelve areas, namely, raw material area, fnished product area, inspection area, heat treatment area, electroplating area, laser engraving area, surface treatment area, CNC turning area, boring machine area, boring and milling area, machining center area, and clamping area, respectively. Enterprise products are mostly military products, statistics in the past three years product orders, and equipment information, the workshop produces twenty-two major products, a total   Figure 6: Te framework of IFOA.

Computational Intelligence and Neuroscience
Trough the investigation of the original workshop layout, we found that the workshop has difculties in workpiece clamping and frequent tooling switching, too much work-in-progress accumulation and low utilization rate of workshop equipment, overlapping logistics routes, and more reverse logistics, which are mainly caused by the continuous increase of product types in the workshop. Te original cluster layout of the workshop is no longer suitable for production. Terefore, the enterprise urgently needs to relayout in order to adapt to the dynamic and variable requirements of multi-variety small batch production. At present, the enterprise has purchased some movable equipment to meet the premise of a dynamic layout.
Based on the above analysis, the layout of the aerospace complex component workshop can be optimized from the following directions. Firstly, according to the group principle, the establishment of product parts' family and the centralized production of products with similar process structure can efectively reduce the number of fxtures switching. Secondly, constructing a manufacturing cell can make the logistics      Computational Intelligence and Neuroscience cross-concentration within the cell and reduce the occurrence of reverse logistics, thus reducing the overall logistics chaos in the workshop and, fnally, concentrating the product in the unit. On the one hand, the fow distance of products is shortened. On the other hand, the utilization rate of unit production equipment and personnel is improved, thus effectively reducing the waiting time of products and further reducing the nonvalue-added time of products.

Product Family Design.
Considering the relatively small number of product types in the production workshops of aerospace enterprises and the special difculty of representing the structure of typical complex components in aerospace, the feature bit code domain method is applied to encode twenty-two major categories of parts in the workshop, considering the part structure, type, main process, volume, weight, and surface treatment, and constructs the product design family [33]. An encoding example is shown in Figure 13, and the code bit domain values are shown in Table 1. As for the previous example, the frst bit indicates whether the part is a rotary body. Since 70% of the aerospace components of this enterprise are nonrotational, 0 indicates a rotary body and 1 indicates a nonrotational. Te second bit indicates that the part belongs to the type; among them, numbers 1 to 6 represent the complex structure frame class, thin-walled shell class, thin-walled complex structure class, disk shaft class, thin-walled plate class, and channel class, respectively. Te third bit indicates the main machining process, and the numbers 1 to 3 indicate turning, milling, and clamping, respectively. Te fourth bit indicates the part size class, where 1 indicates V ≤ 0.5 m 3 , 2 illustrates 0.5 m 3 ≤ V ≤ 1 m 3 , and 3 refers to V ≥ 1 m 3 . Te ffth bit indicates part weight class where numbers 1 to 3 demonstrate W ≤ 5 kg, 5 kg ≤ W ≤ 10 kg, and W ≥ 10 kg, respectively. In clustering, the parts with large volume and small weight or small volume and large weight are more likely to be clustered into a class [34]. Te sixth position indicates the part surface treatment, and the numbers 0 to 3 represent no    I  II  III  IV  V  VI  0  1  1  1  1  1  1  1  2  1  1  1  3 1 4 1 Figure 12: Layout of a typical aerospace production workshop for complex components. treatment required, heat treatment, electroplating, and surface treatment, respectively. Several types of typical aerospace complex components are shown in Figure 14, and the results of constructing product families of typical complex components for twenty-two major categories of aerospace companies are shown in Table 2.
According to the product design family and process fow used to build the product-equipment matrix shown in Table 3, the matrix has a certain degree of process similarity, but one still cannot intuitively determine which parts should be classifed as a manufacturing cell. Terefore, the K-Means++ algorithm is performed to determine the precise clustering of parts to divide the manufacturing cell. Firstly, the elbow method is applied to the product design family to determine the clustering K value, and the results are shown in Figure 15. From Figure 15, we can see that its elbow infection point is fve; that is, the data in this study are clustered into fve classes as the optimal, so K = 5 is substituted into the K-Means++ algorithm, and its clustering results are shown in Table 4 after fnishing.

Dynamic Layout Solution.
Te cell layout of the production workshop consists of twelve areas, which are the raw material area, fnished product area, inspection area, heat treatment area, electroplating area, laser engraving area, surface treatment area, and fve manufacturing cell areas, respectively. Enterprise products are mostly military products, and according to statistics in the past three years for product orders and equipment information, the production workshop produced a total of twenty-two products and a total of thirty-seven sets of equipment, of which the statistical information of each piece of equipment is shown in Table 5. An order cycle of processed products' process route, transport times, and transport batch is shown in Table 6. Among them, the number of transports is determined by the pallet capacity and product orders, independent of the production process route. Based on a comprehensive analysis of the amount of equipment in each manufacturing cell, product types and batches, and product process routes and considering the area of the manufacturing cell, safety      distance between equipment, and workers' operation space, the optimized cell layout of the production plant of an aerospace enterprise is drawn based on SLP, as shown in Figure 16. We note that the related information of processing time is available in our previous work [35]. Taking the manufacturing cell two with the most movable equipment as an example, there are eleven pieces of equipment in its cell, and the processed products are thinwalled shells, cylinder bodies, channel bodies, outer shells, and cases in fve categories, and now, the dynamic reconstruction optimization solution is performed for the equipment layout in cell two. Fifty initial layout solutions are randomly generated and brought into MATLAB for iterative operations, including setting olfactory step length OR � 2         Clamping  table  1  1  1  1  1  1  1  1  1  1  1   Classifcation  result  1  1  1  2  2  2  2  2  3  3  3 Precision   Computational Intelligence and Neuroscience and visual step length VR = 3. Decisions are made at each product switch to determine whether to reconstruct the current layout to ensure the efciency of the system, and the iteration runs for two hundred generations [36]. Moreover, extended experiments between the fast nondominated sorting genetic algorithm (NSGA-II), FOA, and IFOA are conducted. Te iteration diagram of comprehensive cost operation and comprehensive area operation are shown in Figure 17.

Experimental Results.
After twenty independent runs, the satisfactory solutions are no longer signifcantly diferent, and since the cost and area objectives do not confict with each other, the integrated area can also be optimal if the integrated cost is optimal. Terefore, the segmented solution is carried out in this study, and its calculation results are shown in Table 7, where the results obtained by the original FOA and IFOA indicate that cell two needs to be reconstructed, but the reconstructed solution is not found by NSGA-II and CPLEX. At the same time, the original FOA is more accurate than the NSGA-II, but it tends to fall into the local optimum, resulting in poor convergence. Te NSGA-II converges at 122 and 89 generations, respectively, while the original FOA converges only at 158 and 130 generations. Te IFOA can jump out of the local optimum more quickly and converge quickly with high accuracy compared with the original FOA as a result of the random search mechanism which enriches population diversity. By comparing the results of IFOA and CPLEX, the comprehensive cost is reduced by 0.66% and the comprehensive area is reduced by 1.13%. It also verifes the correctness of the mathematical model by comparing results obtained by IFOA and CPLEX.
Te experimental results show that the IFOA outperforms the other three methods in solving multiobjective dynamic facility layout problem. Furthermore, the IFOA is applied to optimize the layout of each manufacturing cell, and the optimized cell layout is shown in Figure 18. It can be found that manufacturing cell two and manufacturing cell four need to reconstruct the     IFOA [1, 2, 11, 4, 5, 6, 10, 3, 8, 7, 9, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0] 18947 87.6 [1, 3, 11, 4, 5, 6, 10, 2, 8, 7, 9, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0] Original FOA [1, 2, 11, 4, 5, 6, 10, 3, 8, 7, 9, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0] 18947 87.8 [1, 8, 11, 4, 5, 6, 10, 3, 2, 7, 9,    the other hand, manufacturing cell four needs to be reconstructed during wing production. Due to the use of vertical machining center JET40 for wing production, equipment is far from the export of the manufacturing cell; it is necessary to exchange the position with the vertical conversion machining center to reduce the logistics cost. As shown in Figure 18, after the optimized cell layout, the logistics distance between workstation 11 and workstation 12 is shortened and no longer blocked by other workstations. Te total cost of the optimized cell layout is CNY 221,516, of which the logistics cost is CNY 205,774, the reconstruction cost is CNY 11,786, and the loss cost during reconstruction is CNY 3,956. Compared with the logistics cost of the existing cluster layout of the workshop of CNY 242,830, the overall optimization is 8.7%. For this enterprise production workshop cell layout scheme compared with the cluster layout scheme, it can efectively reduce logistics costs; with the aerospace enterprise production workshop, product types continue to increase, the workshop existing cluster layout has gradually become unable to meet the production of multivariety, small batch products, so the workshop cell layout has a great application value.

Simulation Verification
Te production workshop of multivariety and small batch aerospace enterprises is a dynamic discrete system. For its production mode of multivariety and small batch products and the characteristics of a complex production process, the simulation becomes an efective tool to solve the production decision problem of this type of enterprise. Compared with the traditional mathematical analysis, the simulation is more suitable for describing the complex logistics system, and the process and results of the simulation can be previewed at the same time. In the enterprise transformation or new workshop layout before, the application of simulation methods for each planning scheme for virtual operation can make the enterprise personnel understand the efect of the scheme in advance, to achieve the comparison and evaluation between the schemes and timely optimization of the scheme adjustment.
To verify the applicability of the proposed reconstruction layout model and the IFOA, we construct a simulation model of an aerospace enterprise production workshop based on plant simulation, conduct simulation analysis of the before and after optimization scheme, identify simulation entities such as products, equipment, and orders, establish simulation logic by applying SimTalk simulation language, solve the problem of dynamic evaluation of workshop reconstruction layout, and realize the simulation of an aerospace enterprise production workshop.

Simulation Model
Establishment. An aerospace enterprise multivariety small batch typical complex components production workshop is taken as the background; the workshop has produced in the past three years a total of twenty-two products and a total of thirty-seven sets of equipment. Te workshop is still using the traditional cluster layout, which has a total of twelve areas, respectively: raw materials area, fnished products area, inspection area, heat treatment area, electroplating area, laser engraving area, surface treatment area, CNC turning     Computational Intelligence and Neuroscience area, boring machine area, boring and milling area, machining center area, and clamping area. After improving the layout of the cells, the workshop has fve manufacturing cells, fve auxiliary cells, and two storage cells, with thirty-eight workers and fve forklifts. At present, single-piece manual transport is used within the cell, and single-piece manual and batch forklift transport are used between cells, where the speed of forklift is 1.2 m/s due to the speed limit. Te aerospace typical complex components production workshop simulation entity is determined according to the above information, where the raw material area uses the source (Source) module for the storage of blank parts. Te area of the fnished product uses the material end (Drain) module for the storage of fnished products. Te rest of the equipment is using the processing station (Station) module for the processing of products and inspection; the establishment of the workshop cluster layout and cell layout simulation is shown in Figures 19 and 20.
Orders are the premise of the production workshop simulation, and by setting reasonable product orders, we can compare the advantages and disadvantages of diferent layout schemes. Since the maximum production capacity of the workshop in a single day is about one hundred sets of components on average, it cannot cover all the products ordered, but the simulation should examine the robustness of the layout; therefore, based on comprehensive product orders in the past three years, all twenty-two kinds of products are brought into the simulation proportionally for a day of production. Simulation of workshop cluster layout and workshop cell layout are carried out separately, and the ratio of their product production, transportation, and storage accounted for and order completion time are counted.

Simulation Output Analysis.
Te same group of aerospace product orders is brought into the simulation model of cluster layout and cell layout, respectively, and the simulation time is recorded when the source module (Source) generates the frst entity, and the forklift transports each blank part to each manufacturing cell, in which the forklift gives priority to the shortest path between two points for distribution, and the shop uses two lanes in both directions to efectively avoid forklift "lockup." In the simulation process, all parameters of the cell layout scheme and the cluster layout scheme are set to the same, and only the location of each piece of equipment is considered diferent.
Te simulation ends when the last product of the order is deposited in the material end (Drain), and the summary report of the cluster layout simulation is displayed in the statistical report module. Te indexes such as simulation optimization time consumed, average time of a single simulation, and number of simulation evaluations for the case are shown in Table 8 using the above algorithm.
After the model simulation is completed, the ratio of product production, transport, storage, order completion time, and workshop area utilization of each solution are compared to arrive at the optimal cell layout solution.
Te calculation method of workshop area utilization is shown in equation (13), the comparison of logistics, reconstruction, and loss costs in the workshop of each scenario is shown in Figure 21, and the comparison of the ratio of production, transport, and storage of workshop products is shown in Figure 22. Te comparison of indicators for each scenario is shown in Table 9: where S i is defned as the area of each cell, S Tract is defned as the area of tract, and S Toatl is defned as the area of total workshop. Compared with the existing cluster layout, the cell layout can efectively increase the ratio of product production in the typical aerospace complex component production workshop. Te use of cell layout can efectively reduce the distance of product transport in the workshop, thus reducing the product transport time, and the product transport is mostly concentrated in the cell, which can realize singlepiece fow production in each manufacturing cell, thus effectively reducing the confusion of workshop logistics. At the same time, the similar structure of products in each cell can efectively reduce the number of product mold changes and shorten the production preparation time, thus reducing the product storage time and the number of work-in-process, which verifes the superiority of the U-shaped cell reconstruction layout optimization model proposed in this study and the applicability of the proposed IFOA.

Conclusion
In this paper, we study the optimization problem of reconstruction layout of multivariety small batch production workshop of aerospace typical complex components.
(1) A manufacturing cell layout planning method based on the feature bit code domain method and K-Means++ is proposed to realize the accurate division of manufacturing cells. (2) A multiobjective optimization model of manufacturing cell reconstruction layout with the optimization objectives of logistics cost, reconstruction cost, loss cost, and integrated area of the cell is established, and a novel IFOA is presented to solve the model. Computational Intelligence and Neuroscience