# A Facility Layout Algorithm for Logistics Scenarios Driven by Transport Lines
## 4 Experimental Results and Analysis  
### Experimental Design  
In order to verify the effect of force-directed on the layout of logistics scenes and determine the optimal combination of MOSA and force-directed, this paper applies force-directed to MOPSO, NSGAII, and mixed integer programming (MIP) respectively, forming MOPSO-FD, NSGA-FD and MIP-FD algorithms. The four multi-objective algorithms are tested separately by comparison experiments, in which each algorithm is run independently for 10 times, and the parameters of the algorithms are kept consistent for each run. Therefore, the number of iterations for each algorithm is determined based on the scale, with 100, 80, and 50 iterations used for different sizes while ensuring that the running time of each algorithm is kept in check. The known information of the workshops, facilities, and lines of each instance is shown \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Transport Line** & **Unit Cost** \\ \hline  & workshop entrance 1—facility 1 & \\  & (1/1)—facility 2 (1/1)—facility 3 & \\  & (1/1)—facility 5 (1/1)—facility 11 & \\  & (1/1)—facility 5 (1/1)—facility 11 & \\  & entrance 1 & \\  & & entrance 1 & \\  & & workshop entrance 1 -facility 1 & \\  & & entrance 1 & \\  & & entrance 1 & \\  & & entrance 1 & \\  & & entrance 1 & \\  & & entrance 1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Instance 2 line data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Type** & **Length** & **Width** & \begin{tabular}{c} **Entrance** \\ **Coordinates** \\ \end{tabular} & \
\begin{tabular}{c} **Exit** \\ **Coordinates** \\ \end{tabular} &
\begin{tabular}{c} **RGB Values** \\ **RGB Values** \\ **RGB Values** \\ \end{tabular} \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Instance 3 facilities data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Transport Line** & **Unit Cost** \\ \hline  & workshop entrance 1—facility 1 & \\  & (1/1)—facility 4 (1/1)—facility 5 & 3, 1, 2, 1 \\  & (1/1)—facility 6 entrance 1 & \\  & workshop entrance 1—facility 2 (1/1) - & \\
2 & facility 3 (1/1)—facility 5 (2/2)—facility 6 & 2, 2, 1, 3 \\  & entrance 2 & workshop entrance 1—facility 1 & \\
3 & (1/1)—facility 3 (1/1)—facility 5 & 3, 1, 2, 1 \\  & (1/1)—facility 6 entrance 1 & \\
4 & facility 6 exit 1—workshop exit 1 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Instance 1 line data. There four algorithms proposed in this paper is validated for its performance through layout instances of different scales. The layout instance of a small-scale consists of six facilities, one workshop entrance, and one workshop exit. The layout instance of a medium-scale consists of 12 facilities, 2 workshop entrances, and 1 workshop exit. The layout instance of large-scale consists of 25 facilities, 5 workshop entrances, and 5 workshop exits. Experiments run on Intel(R) Xeon(R) CPU E5-2609 v4 1.70 GHz CPU, 16 GB RAM. Each algorithm is implemented using Python 3.6. The horizontal distance \(h_{min}\) and vertical distance \(v_{min}\) of the workshop are 2; the distance \(d\) between the facility and the transport line is 2; and the unit cost of the linear conveyor \(c_{s}\) and the unit cost of the turning conveyor \(c_{t}\) are 100 and 2000, respectively. The MOSA-FD algorithm uses 80 iterations for neighbor finding, with the initial temperature set to 10,000 and a cooling rate of 0.9. In contrast, the parameters of the MOPSO-FD algorithm include a particle population size of 100, \(C_{1}\) and \(C_{2}\) values of 0.5, and a \(W\) value of 0.5. The NSGAII-FD algorithm is configured with a population size of 100, a crossover rate of 0.8, and a mutation rate of 0.2. Among them, the force-oriented algorithm is iterated a total of 16 times, with a facility repulsion weight \(\alpha\) of 0.6 and a boundary repulsion weight \(\beta\) of 0.4. Additionally, the attractive force coefficient \(k_{t}\) is set to 1, while the repulsive force