# A Facility Layout Algorithm for Logistics Scenarios Driven by Transport Lines
## 4 Experimental Results and Analysis
### Layout Analysis  
Figures 12-14 represent the layout result plots of each algorithm for different scale instances, respectively. The solution space of the facility layout problem increases with the number of facilities. Since the non-transport line-driven layout algorithms (NSGA II, MOPSO, MOSA, and MIP) fail to effectively use the information of known transport lines, resulting in a scenario where the facility locations can only be generated randomly, it is impossible to find a reasonable area for the layout of facilities in the workshop with a large solution space. Moreover, the layout outcomes often contain excessive turning points and the workshop space is divided into multiple small areas due to the presence of transport lines. This can result in limited mobility for the staff within the facility. In contrast, the layout of facilities and transport lines based on the transport line-driven layout algorithms (NSGA II-FD, MOPSO-FD, MOSA-FD, and MIP-FD) is more reasonable, the activity space in the workshop is more open, and this characteristic is more obvious as the scale of the layout instance increases. The transport line drive algorithm exhibits significantly shorter transport lines than the non-transport line-driven method, and there is no need for bypassing. As a result, this approach performs better in terms of cost metrics. By comparing the layout solutions of MOSA-FD algorithm and MIP method, it is obvious to find that MOSA-FD algorithm belongs to free-space layout, which has fewer constraints on the coordinate position of the facilities, and the logistics relationship of the facility layout will be more closely driven by force direction. While the MIP method belongs to the multi-row facility layout, the same row of facilities will be in the same coordinate area, and the lines of the layout solution are greatly influenced by the location of the facilities, which makes it difficult to discover the logistic relationship of the layout solution.  
Figure 11: Histogram of data for each algorithm at each instance. **(a)** Instance 1 of each algorithm metric; **(b)** instance 2 of each algorithm metric; **(c)** instance 3 of each algorithm metric; **(d)** instance 1 optimization ratio of transport line-driven algorithm; **(e)** instance 2 optimization ratio of transport line-driven algorithm; and **(f)** instance 3 optimization ratio of transport line-driven algorithm.  
Figure 12: Layout plots of each algorithm at instance 1. (**a**) NSGA II-FD; (**b**) MOPSO-FD; (**c**) MOSA-FD; (**d**) MIP-FD; (**e**) NSGA II; (**f**) MOPSO; (**g**) MOSA; and (**h**) MIP.  
Figure 13: Layout plots of each algorithm at instance 2. (**a**) NSGA II-FD; (**b**) MOPSO-FD. (**c**) MOSA-FD; (**d**) MIP-FD; (**e**) NSGA II; (**f**) MOPSO; (**g**) MOSA; and (**h**) MIP.  
Figure 15 shows the simulation diagrams corresponding to the layout scheme of logistics facilities using MOSA-FD algorithm on three instances respectively, according to which it can be seen that a strong facility correlation exists between the transport line-driven layout diagrams. The facilities with a logistics relationship are closely connected, the material transportation distance is shorter, and the target cost of the solution can be optimized. Therefore, the MOSA-FD model-driven logistics facility layout algorithm can be highly valuable for practical application in workshop layouts.