## 2 Methods
### ANN Prediction Modeling  
#### 2.3.1 Latin Hypercube Sampling (LHS)  
The design space refers to the range of all possible values of decision variables, and the optimization algorithm needs to search in the design space for the optimal design solutions. To improve the accuracy of ANN model, a dataset that covers the design space need to be generated for ANN training and validation. A good coverage of the design space can be achieved with a small sample by adopting Latin Hypercube Sampling (LHS) [26], which is a stratified random sampling method. According to [PERSON] et al., a sample size of 1.5-10 times of the number of input variables is enough when using this method [25].  
In this study, 200 samples were generated by LHS, as 20 times of the number of the decision variables, and the process was completed by the Latin Hypercube Sampling module as shown in Figure 5. The Grasshopper plug-in named Design Space Exploration (DSE) was used for sampling in this module. The sampler component of the DSE can automatically generate a nested list of decision variables that span the design space being explored based on the selected sampling technique [38]. There are three optional sampling methods, namely, random sampling, grid sampling and LHS, which were adopted in this study. The generated samples were indexed by the order to be output into other program modules.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type Number** & **Insulation Material and Thickness** & **Average-Value 1** & **AverageU-Value 1** & **Unit Price 2** \\ \hline
**Unit** & **-** & **m2K/W** & **W/m2K** & **\%/m2** & **\%/m2** \\ \hline
0 & Rock wool board (65 mm) & 2.03 & 0.49 & 124 & 17.7 \\
1 & Rock wool board (75 mm) & 2.28 & 0.44 & 128 & 18.3 \\
2 & Rock wool board (90 mm) & 2.58 & 0.39 & 135 & 19.3 \\
3 & Rigid polyurethane board (35 mm) & 2.03 & 0.49 & 165 & 23.6 \\
4 & Rigid polyurethane board (40 mm) & 2.38 & 0.42 & 175 & 25.0 \\
5 & Rigid polyurethane board (50 mm) & 2.58 & 0.39 & 195 & 27.9 \\
6 & Expanded polystyrene board (60 mm) & 2.03 & 0.49 & 110 & 15.7 \\
7 & Expanded polystyrene board (70 mm) & 2.33 & 0.43 & 112.5 & 16.1 \\
8 & Expanded polystyrene board (80 mm) & 2.63 & 0.38 & 115 & 16.4 \\ \hline \hline \end{tabular}  
* Data from [35]. 2 Data according to the Changchun engineering information supervision platform [36].  
\end{table}
Table 2: Thermal and price properties of wall construction types with different insulations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**TypeNumber** & **Window Panel Type** & **U-Value 1** & **SHGC 1** & **VT 1** & **Unit Price 2** \\ \hline
**Unit** & **-** & **W/m2K** & **-** & **-** & **\%/m2** & **\%/m2** \\ \hline
0 & Double pane of clear glass & 2.87 & 0.76 & 0.80 & 60 & 8.6 \\
1 & Triple pane of clear glass & 2.00 & 0.66 & 0.71 & 90 & 12.9 \\
2 & Single silver low-e coating & 2.04 & 0.54 & 0.76 & 120 & 17.1 \\
3 & Double silver low-e coating & 1.96 & 0.40 & 0.69 & 170 & 24.3 \\ \hline \hline \end{tabular}  
* Data from [37]. 2 Data according to the Changchun engineering information supervision platform [36].  
\end{table}
Table 3: Thermal, optical and price properties of different window panel types.