## 2 Methods
### Optimization Design Problem Determination
#### 2.2.2 Optimization Objectives  
This study aimed at reducing building energy consumption and financial cost while ensuring the maximization of indoor daylight quality. The energy consumption is known to have a conflict with daylighting quality in the severe cold region. Commonly, less energy will be consumed by reducing the WWR value, but there is a high possibility of a worse daylighting quality. Bringing daylight into the indoor environment has a significant effect on the occupants' health and well-being [31], especially in the library as the reading environment can be highly improved by well-designed daylighting. The building envelope plays a key role in improving building energy efficiency and daylighting quality, many researchers have focused on building envelope optimization. As financial factors are considered, the design of the building envelope becomes more complex, and a balance must be found between the capital cost and energy efficiency of the building envelope [10]. Therefore, in this study the optimization objectives were to minimize the Energy Use Intensity (EUI), maximize the Spatial Daylight Autonomy (sDA), maximize the Useful Daylighting Illuminance (UDI) and minimize the Building Envelope Cost (BEC). As explained above, incorporating dynamic building simulation in the optimization process is inefficient and complex, so the objective functions related to the building performance simulation were calculated according to the values predicted by ANN models. The specific objective functions were set as follows:  
1. Energy Use Intensity (EUI) EUI was defined as the annual energy consumption per unit area of the buildings, with a metric of kWh/m\({}^{2}\)[15]. Annual cooling load, annual heating load, annual artificial lighting load and annual equipment load of the building were considered. The lower the EUI value is, the better the building energy performance will be. The relevant objective function can be described as: \[\text{Min}f_{1}=\text{EUI}\] (1)
2. Spatial Daylight Autonomy (sDA) sDA is defined as the percentage of floor space where a minimum light illuminance level can be completely met by daylight for 50% of the working hours [16]. sDA considers not only the temporal but also the spatial dynamics of daylight in buildings [32]. In this study, 300 lx is chosen as the minimum daylight illuminance level for sDA. With a higher sDA value, more floor area will meet the daylight illuminance of 300 lx during the analysis period, and the relevant objective function can be described as: \[\text{Min}f_{2}=1/\,\text{sDA}\] (2)
3. Useful Daylighting Illuminance (UDI) UDI is defined as the annual occurrence percentage of daylight illuminances that falls within a given range at the given points [33]. The lower threshold of UDI is 100 lx and incorporates an upper threshold of 2000 lx. Daylight illuminances less than 100 lx are generally considered insufficient for the occupants, and higher than 2000 lx will lead to  
Figure 3: The initial form of the reference building.  
glare and unwanted solar gains. A higher UDI value indicates a better daylighting performance. The relevant objective function can be described as: \[\text{Min}f_{3}=1/\text{UDI}\] (3)
4. Building Envelope Cost (BEC) In this study, BEC includes three parts: the exterior wall cost, the exterior window cost and the roof cost. The optimization process aims to minimize the BEC value and the relevant objective function is: \[\text{Min}f_{4}=\text{C}_{wall}+\text{C}_{window}+\text{C}_{\text{roof}}\] (4) where \(\text{C}_{wall}\) is the index for the cost of exterior walls, \(\text{C}_{window}\) refers to the cost of window panels and \(\text{C}_{\text{roof}}\) refers to the cost of roofs. \(\text{C}_{wall}\), \(\text{C}_{window}\) and \(\text{C}_{\text{roof}}\) are calculated by multiplying the corresponding unit price and the area of exterior walls, window panels and roofs respectively.