## 2 Methods
### ANN Prediction Modeling
#### 2.3.4 ANN Modeling and Training  
Before developing the ANN models, the 200 groups of samples were normalized and divided randomly into two parts: 120 groups of training data and 80 groups of validation data. The Crow plug-in is an architect-friendly ANN modeling tool, which offers the Backpropagation (BP) algorithm for ANN training, only 3 parameters of the Layer Structure (LS), Neuron Count (NC) and Learning Rate (LR) were used to develop an ANN model, also a training cycle (C) parameter needs to be defined for ANN training.  
However, manual adjustments of these parameters still lead to a high probability of inaccurate prediction models. To improve the ANN modeling efficiency and ensure high precision, a multiobjective optimization process was performed using the Octopus plug-in. Octopus adopts the Strength Pareto Evolutionary Algorithm 2 (SPEA2) in combination with the Hypervolume Estimation Algorithm (HypE) for multiobjective optimization. The SPEA2 algorithm is a robust and efficient multiobjective evolution algorithm (MOEA), sharing a similar performance with the widely adopted NSGA-II algorithm [41]. HypE algorithm, which is based on the hypervolume indicator, is highly effective for many-objective problems in comparison to existed MOEAs [42]. As there were two objectives, namely, the minimized Mean Square Error (MSE) between the prediction and simulation results of the training data as well as the maximized correlation coefficients (R) between the prediction and simulation results of the  
Figure 8: Energy and Daylight Simulation module.  
validation data, the SPEA2 reduction method was chosen to combine with the default mutation strategy in the optimization process. The NC, LR and C parameters of the ANN were optimized, and the LS parameter was not considered by the optimization process, as the structure of the 0--sigmoid layer performed significantly better than the other options in this case and was set as a fixed parameter. Considering that the optimization engine always tries to minimize objective function values, MSE and 1/R were used for evaluation of objectives. When the optimization engine stopped, a trained ANN prediction model could be obtained. A preliminary experiment suggested that developing an ANN model for each objective could achieve higher prediction accuracy than one ANN model for three objectives in this case. Hence, three ANN models of EUI, sDA and UDI were trained and optimized, and then saved as the output data in the.cnw file format. The ANN Modeling and Training module is shown in Figure 9.  
In this study, the final MSE values, which represent the average squared difference between the ANN prediction results and the simulation results of the training data, were 0.001 for EUI, 0.0009 for sDA and 0.001 for UDI. The MSE results indicated that the ANN models could perform well on the prediction ability. The reliability of the prediction models was further verified by the regression between ANN prediction results and EnergyPlus simulation results of the validation data, as shown in Figure 10. The R values of EUI, sDA and UDI were 0.973, 0.986 and 0.983 respectively, which proved that the prediction results were in agreement with the simulation results and the ANN models were good enough to surrogate the energy and daylight simulation models.  
Figure 9: ANN Modeling and Training Module.