# A Facility Layout Algorithm for Logistics Scenarios Driven by Transport Lines
## 4 Experimental Results and Analysis
### Experimental Design
Through the comparison of the frontier plots, similar to Figure 9, the transport line-driven layout algorithms (MOSA-FD, NSGAII-FD, and MOPSO-FD) exhibit lower MHC and TFC objective costs compared to the non-transport line-driven layout algorithms (MOSA, NSGAII, and MOPSO). This significant cost difference can be attributed to the traction effect of the force-directed algorithm. However, due to modifications in some metaheuristic parameters, the MOSA-FD, NSGAII-FD, and MOPSO-FD algorithms demonstrate larger cost fluctuations and overall higher layout costs compared to the results in Figure 9. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**MHC**} & \multicolumn{3}{c}{**TFC**} & \multicolumn{3}{c}{**TIME**} \\ \cline{2-10}  & & **Worst** & **Best** & **Average** & **Worst** & **Best** & **Average** & **Worst** & **Best** & **Average** \\ \hline \multirow{3}{*}{2} & MIP-FD & 596.29 & **537.53** & 586.75 & 447.19 & **395.23** & 432.63 & 152.95 & 126.84 & 130.36 \\  & MIP & & 802.11 & & & 790.14 & & & **80.7** & \\ \hline \multirow{3}{*}{3} & MIP-FD & 1294.67 & **1043.34** & 1124.57 & 1159.41 & **960.45** & 1073.7 & 383.22 & 332.09 & 354.43 \\  & MIP & & 1927.62 & & & 6648.15 & & & **273.57** & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _Cont._Figure 11a-c shows the histograms of the results of the three transport line-driven based layout algorithms for different scale instances. For the time performance, MOSA-FD exhibits a better average running time than the other algorithms since NSGAII-FD and MOPSO-FD are population-based optimized algorithms, which entail conducting force-directed local search and constraint detection and processing operations for each solution in the population. However, the MOSA-FD algorithm is based on the current solution only, and the target solution is obtained through the neighbor finding operation and force-directed algorithm processing. For the objective performance, the MOSA-FD algorithm demonstrates superior performance in terms of average MHC and TFC objective values, which further validates the effectiveness of the multi-objective optimization mechanism proposed in this paper. Figure 11d-f shows the histograms of the optimization ratios of three transport line-driven layout algorithms at different scale instances. Taking the results of layout instance 3 as an example, based on the average metrics data of MHC, TFC, and TIME, it can be found that the metrics optimization ratios of NSGAII-FD compared to NSGAII are 30%, 76%, and 37%, respectively; the metrics optimization ratios of MOPSO-FD compared to MOPSO The proportions are 44%, 81%, and 37%, respectively; and the metrics optimization proportions of MOSA-FD compared with MOSA are 36%, 80%, and 47%, respectively, indicating that the force-directed algorithm can significantly improve the performance of logistics facility layout algorithms. Figure 10: The Pareto optimal frontier plots for contrast parameters. (a) Instance 1; (b) instance 2; and (c) instance 3. Figure 9: The Pareto optimal frontier plots. (a) Instance 1; (b) instance 2; and (c) instance 3.