## 5 Computation Experiments
### Experimental Analyses  
Figure 12 shows the convergence curves of three objectives, and these curves start to converge in the 280 th generation. The Pareto solutions' distributions of the final generation are shown in Figure 13, in which the same pareto solutions are plotted only once, and it can be seen that the Pareto solution set has a good distributivity. Thus, it can provide a wide range of alternative choices for the managers.  
Moreover, Table 5 displays the three objectives and corresponding energy consumption components of part solutions in the Pareto solution set, where these solutions are ranked in non-increasing order of _TEC_. Figures 14 and 15 give the scheduling gantt chart and workshop layout of solution 1, respectively, which shows that these solutions are logical and feasible. It can be seen that although the _TEC_ of solution 1 is minimal in Pareto solutions, its energy consumption components (_PE_, _IE_, and _TE_) are not all minimal. This phenomenon implies that coordinated optimization of scheduling and layout planning is extremely important to reduce energy consumption for workshops.  
Figure 14: The Gantt chart of solution 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Solution** & \(C_{\text{max}}\) **(min)** & _TEC (kw/h)_ & _MHQ (kg)_ & _PE (kw/h)_ & _IE (kw/h)_ & _TE (kw/h)_ \\ \hline
1 & 23.4752 & 853.0703 & 82.8975 & 562 & 83.8266 & 207.2437 \\
2 & 23.4752 & 853.2411 & 82.9660 & 562 & 83.8260 & 207.4151 \\
3 & 23.5124 & 857.1738 & 73.6347 & 592 & 81.0870 & 184.0868 \\
4 & 23.4751 & 866.7355 & 88.3640 & 562 & 83.8254 & 220.9101 \\
5 & 23.4794 & 871.7218 & 79.5463 & 592 & 80.8560 & 198.8658 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
46 & 33.3751 & 1133.8233 & 24.9989 & 952 & 119.3260 & 62.4973 \\
47 & 33.3750 & 1148.3944 & 27.4677 & 954 & 125.7250 & 68.6693 \\
48 & 33.3838 & 1156.5963 & 23.0329 & 978 & 120.9869 & 57.5823 \\
49 & 33.3769 & 1158.3316 & 24.8773 & 978 & 118.1384 & 62.1932 \\
50 & 33.3750 & 1188.4205 & 26.4382 & 1004 & 118.3250 & 66.0955 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The Pareto set.  
Figure 13: The Pareto solutions’ distribution for three objective functions.  
In order to further analyze the relationship between _TEC_ and corresponding energy consumption components (_PE_, _IE_, and _TE_), this paper uses the _TEC_ of the Pareto solution set as the horizontal coordinate and the corresponding energy consumption components as the vertical coordinate to draw the distribution curve of each energy consumption component, as shown in Figure 16. It can be seen that the _PE_ and _TE_ curves are relatively stable, while the _IE_ curve shows remarkable fluctuation. This is because the scheduling and layout planning determine the values of _PE_ and _TE_, respectively, while the value of _IE_ is affected by the scheduling and layout planning, which leads to the obvious fluctuation of the _IE_ curve.  
Moreover, in Figure 16, it is noted that the _PE_ curve and _TE_ curve correspond to a trough and a peak, respectively, when the _TEC_ is about 900 kw/h. In order to explain this special phenomenon, the solutions related to this phenomenon are shown in Table 6. Figures 17 and 18 show the scheduling gamtt chart and workshop layout of the solution 13 in Table 6, respectively. Comparing Figure 14 with Figure 17, it can be found that although the _C_max and _PE_ of solution 13 are less than solution 1, the _TEC_ of solution 13 is still greater than that of solution 1. This is because each operation in solution 13 chooses the machine with a minimum processing time, which causes jobs to move frequently between machines, resulting in excessive _TE_ and _MHQ_. Therefore, the _PE_ and _TE_ curves generate the peak-trough correspondence phenomenon. The phenomenon further illustrates that the coordinated optimization of scheduling and layout planning can not only quick respond to the changes of market demand, but also balance the production efficiency and energy consumption of enterprises.