# Safe Three-Dimensional Assembly Line Design for Robots Based on Combined Multiobjective Approach
## 4 Experimental Results and Analysis
### Case Study of Safe Layout  
An automotive assembly line is selected as an example, in which the diversity of safety layout, safety, and economic benefits has been verified. The assembly line has ten pieces of equipment, including three robots. Table 4 shows the equipment information. In the planning period t from M\({}_{\text{i}}\) to M\({}_{\text{j}}\), D\({}_{\text{ij}}\) is the distance. Table 5 presents the material transportation cost per unit distance C\({}_{\text{ij}}\) during period t. Table 6 lists the demand for the assembly parts P\({}_{\text{ij}}\). The available layout area length is L = 22 m, the width is W = 12, and the line spacing is A = 1 m. The distance from the first line to the available edge is A0 = 1.5 m. The net distance between two facilities is \(\delta_{\text{ij}}\in\) [0.1, 1.8]. The actual maximum motion range of the robotic arm is 5.2 m, which is shy of the rated maximum motion range of 5.4 m, as shown by the assembly range of the cloud points in Figure 3. The assembly line includes the KUKA KR210 R2700 robots M4, M5, and M6, with a maximum working radius of 2.7 m and a robot base radius of 0.33 m. The experimental environment is Windows 10 system, Python 3.7.1, and Anaconda3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **E \({}^{1}\)** & **F \({}^{2}\)** & **N \({}^{3}\)** & **R\({}_{0}\), R\({}_{\text{max}}\) (m)** & **Size (L, W(m))** \\ \hline M1, M2, & & Processing & & & \\ M10 & M \({}^{4}\) & & Workpiece & & & \\ M3, M8, & & & & & \\ M9 & & & & & \\ M4 & R \({}^{6}\) & Grab & 1 & 0.33, 2.7 & 2.6, 0.66 \\ M5, M6 & R \({}^{6}\) & Grab Assembly & 2 & 0.33, 2.7 & 2.6, 0.66 \\ M7 & M \({}^{4}\) & Combine Processing & 1 & 0, 0 & 8, 2.6 \\ \hline \hline \end{tabular}  
\({}^{1}\) E (equipment); \({}^{2}\) F (function); \({}^{3}\) N (number); \({}^{4}\) M (machine); \({}^{5}\) S (station); \({}^{6}\) R (robot).  
\end{table} 
Table 4: Equipment information. Figure 5: Statistical results of the Pareto front in comparison. Table 7 shows the process routes of the three assembly parts. The process quality, throughput, success rate, and downtime are assumed to be ideal. The process elements include machines and workstations. There is no robot for the P1 process element. For P2, M5, and M6 robots take the workpiece from the machine for cooperative assembly. In the process for P3, the M5 and M6 robots take the workpiece from the machine and perform the assembly. Many researchers have verified that heuristic algorithms and heuristic algorithms are effective in solving the layout design problem. The proposed approach was compared with two mainstream multiobjective optimization methods. NSGA-II [8], MOCell [38], and SE-NSGA2 are used in order to solve the safety layout design of the assembly line. Optimization object is the same assembly line, and the compared environment is fair. The diversity of a safe assembly line layout is verified. Comparative experiments prove that the safe layout model and SE-NSGA2 approach can effectively increase the number of optimal layout plans. Table 8 shows the statistical results of the experiment over 30 independent runs. The data in the table indicate that the SE-NSGA2 approach is superior to other methods based on the number of optimal plans and diversity of plans. The comparison experiment uses the general layout model (GLM) [17] and the safety layout model (SLM). When optimizing an assembly line layout with robots, if only the maximum working range of each robot is considered, then collaborative assembly cannot be achieved. Therefore, the comparison experiment selects the robot base as the optimized entity in order to ensure the operation requirements of collaborative assembly. In the general layout model, the Pareto optimal plans of three algorithms have little difference in percentage, but the Pareto solutions of SE-NSGA2 are not superior to others of diversity. The results are related to the determination of safety indicators in the proposed approach. The general layout model does not consider the assembly collaboration of