## 3 Testing with a Simple Room Case
### Test Method
#### 3.3.2 Based on Experimental Data and 3D Simulations  
The inverse predictions are based on experimental data and 3D simulations. Some of the particular non-dominated solutions generated in NSGA-II using continuous populations (continuous optimization) or discrete populations (discrete optimization) are shown in Table 3. Figure 6 shows the Pareto Frontiers. Because of the differences between experiments and simulations, inverse predictions based on experimental data are more likely to be biased. According to the stopping criteria (Within \(s\) consecutive iteration steps, \(F^{\prime}_{min}\) remains constant) in Section 2.5, the optimization should have been stopped before Iteration 39, but the optimization was continued because the inverse prediction was not satisfactory (the deviation of the solution corresponding to \(F^{\prime}_{min}\) is still large). In order to determine if a better outcome might be reached, a bigger \(s\) was used. However, it was shown to be difficult for this case. The authors analyze some reasons for this, using \(F_{1}\) as an example: \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **No.** & \(\begin{array}{c}V_{in}\text{ (m/s)}\\ \text{ (Deviation)}\end{array}\) & \(\begin{array}{c}T_{in}\text{ (}^{\ast}\text{C)}\\ \text{ (Deviation)}\end{array}\) & \(\begin{array}{c}F_{1}\end{array}\) & \(\begin{array}{c}F_{2}\end{array}\) & \(\begin{array}{c}F^{\prime}\end{array}\) \\ \hline Iteration 39 & 1 & \begin{tabular}{c} 0.61033 \\ (continuous) \\ \end{tabular} & \begin{tabular}{c} 16.43050 \\ (7.075\%) \\ 2 \\ \end{tabular} & \begin{tabular}{c} 0.05569 \\ (7.075\%) \\ 2 \\ \end{tabular} & \begin{tabular}{c} 0.02771 \\ (7.5\%) \\ 16.63695 \\ \end{tabular} & \begin{tabular}{c} 0.04170 \\ (min) \\ 0.13114 \\ \end{tabular} & \begin{tabular}{c} 0.04170 \\ (min) \\ 0.01539 \\ (min) \\ 0.02668 \\ \end{tabular} & \begin{tabular}{c} 0.04170 \\ (min) \\ 0.04109 \\ (min) \\ 0.04013 \\ (min) \\ 0.07327 \\ \end{tabular} \\ Iteration 12 & 1 & \begin{tabular}{c} 0.59 \\ (3.51\%) \\ 0.76 \\ \end{tabular} & \begin{tabular}{c} 16.5 \\ (10.0\%) \\ 16.6 \\ \end{tabular} & \
\begin{tabular}{c} 0.05497 \\ (min) \\ 0.01565 \\ (min) \\ 0.12294 \\ \end{tabular} &
\begin{tabular}{c} 0.04075 \\ (min) \\ 0.01565 \\ (min) \\ 0.06930 \\ (min) \\ 0.06930 \\ \end{tabular} \\ \hline \end{tabular}  
Notes: Based on experimental data and 3D simulations.  
\end{table} 
Table 3: Part of Pareto solutions and the objective function values. Figure 6: The Pareto Frontiers in three situations. Figure 7 shows the presence of a sudden change in \(F_{1}\) (samples with a red label--\(F_{1}>0.7\); samples with a blue label--\(F_{1}<0.3\)), corresponding to the inversion of the flow field in this case [55]. This also reveals that there are some abrupt changes in the air delivery optimization, contrary to most of the optimizations performed based on the continuity assumption. As the Kriging method is also a smooth interpolation method, this dictates that the method may not handle this problem well. But this problem is not the most important (according to Section 3.3.1, when facing this problem, the results obtained from inverse prediction based on 2D simulation are still accurate). A more critical problem is that the results of 3D steady-state simulations are usually unstable; any physical quantity at any position usually fluctuates and does not converge to a stable value as in a 2D steady-state simulation. As Figure 8 shows, although 2000 iteration steps were used to average the velocity values for each location, \(F_{1}\) still had rapid and irregular changes in some areas. The large gradient caused the OK models to believe that the minimum value would be generated in these areas. So, the filling process always took place in these areas. For this 3D inverse prediction, from Iteration 20 to Iteration 39, most of the new samples were in  
In other words, the problem expressed above is that the results of 3D steady-state simulations are usually unstable, so that the response values have both 'global' and 'local' variation.