# Study on Multi-Objective Optimization-Based Climate Responsive Design of Residential Building
## 4 Discussion of Optimization Results
### Optimization Results of Residential Buildings in Typical American Cities
In general, the main goal of the public social sector is to vigorously reduce energy consumption and pollution emissions, while the goal of private households is mainly to save costs and achieve indoor thermal comfort. Therefore, in Figure 14. BED-GC non-dominated solutions focus on analyzing the minimization of BED and GC. These solutions are part of the 3D non-dominated solution because there is no other solution to improve (i.e., reduce) BED and GC at the same time. Through the BED-GC Pareto Frontier, it is easy to know:  
* \"Energy-saving optimal (nZEB) solution,\" that is, BED is minimized in all non-dominated solutions, located at the right end of the 2D Pareto frontier of Figure 15. Although this solution is expressed as nZEB, it does not mean it meets the specific nZEB standard, but because this solution is a non-dominant solution with the lowest energy demand, and its performance is closest to the nZEB standard. * \"Cost optimal (C-O) solution,\" that is, the GC is minimized among all non-dominated solutions, located at the left end of the 2D Pareto frontier of Figure 15.
* \"nZEB' solution,\" when neither \"energy-saving optimal (nZEB) solution\" and \"cost optimal (CO) solution\" can meet the requirements of comprehensive indicators, in order to obtain a compromise result, it is necessary to introduce \"nZEB' Solution,\" compared to the reference design, \"nZEB' solution\" has lower GC and BED values (see Figure 16). Figure 15: Building energy demand (BED, vertical axis) and global cost (GC, horizontal axis) Pareto frontier in typical American cities. From the analysis of the optimal objective function value in Table 14, it can be seen that except Los Angeles, from warm climate zone to cold climate zone, the BED value gradually increases, because in the calculation of energy demand, heating demand is higher than cooling demand. Specifically, in nZEB optimal solution, BED in Houston is 36.20 kWh/m\({}^{2}\), GC is 286.97 $/m\({}^{2}\), DH is 29.17%, whereas in Fairbanks, BED is 114.54 kWh/m\({}^{2}\), GC is 418.76 $/m\({}^{2}\), DH is 53.33%. In C-O optimal solution, BED in Houston is 53.45 kWh/m\({}^{2}\), GC is 256.26 $/m\({}^{2}\), DH is 41.67%, whereas in Fairbanks, BED is 162.55 kWh/m\({}^{2}\), GC is 347.76 $/m\({}^{2}\), DH is 61.67%. Whereas in Los Angeles, because of its climate characteristic, the energy demand is relatively lower than other cities. According to nZEB and C-O optimal solutions, Table 12 lists the design parameters of residential buildings in different climate zones. In all optimization schemes, the best building orientation is the east-west orientation (0\({}^{\circ}\)), in order to facilitate the building to make maximum use of solar radiation in the colder season. As far as the optimization of the envelope parameters is concerned, the solar absorbance of the roof and external wall gradually increases from the warmer climate zone to the colder climate zone to maximize the utilization of solar radiation. For example, the solar absorbance of the roof and external wall in Houston residential building that is located in the south of the United States, is between 0.1 and 0.2, while that in Duluth and Fairbanks which are in the north of the United States are between 0.75 and 0.9. The change in the thickness of envelope insulation is also related to the latitude of the city. The optimal solution for the US climatic zone 2 and climatic zone 3 represented by Houston and Los Angeles respectively does not recommend the use of insulation layers on roofs, external walls, and ground floors because these cities are in the southern United States. Compared with thermal insulation, it pays more attention to heat dissipation in summer. Therefore, the nZEB optimal solution in Houston and Los Angeles recommends the use of bricks with larger heat capacity on the building envelope. The thermal conductivity and density of the roof and ground floor bricks are 0.72 W/mK and 1800 Kg/m\({}^{3}\), 0.9 W/mK, and 2000 Kg/m\({}^{3}\) in Houston.