## 3 Results and Discussions
The BEC values of the non-dominated solutions were centrally distributed between 2.03\(\times\)10\({}^{6}\) and 2.35\(\times\)10\({}^{6}\), with a median of 2.20\(\times\)10\({}^{6}\). As the samples can represent the feasible solutions, the results indicate that the overall performance of the non-dominated solutions was better than that of the feasible solutions, which proved that the proposed method was highly effective. Figure 13: Matrix plot of non-dominated solutions and correlation coefficients between objectives. Three relative optimal solutions were selected from the non-dominated solution set, which have achieved high performance and tradeoffs among four objectives. The decision variables of the original design and the relative optimal solutions are shown in Table 6, while the optimization objectives of them are shown in Table 7. From Table 6 we can see that the decision variables of the original design were obviously different from that of the relative optimal solutions, but the three relative optimal solutions had more similarities with each other. The H in this table refers to the floor height variable. The window and skylight variables were the flat skylight width (W), widths of arched window A (W\({}_{\text{a}}\)) and arched window B (W\({}_{\text{b}}\)), widths of strip window 1 (W\({}_{1}\)), strip window 2 (W\({}_{2}\)), strip window 3 (W\({}_{3}\)), as well as sloped roof skylight width (d). T\({}_{\text{wall}}\) refers to the wall construction type, the integer 0 represents that the insulation layer of the wall is the rock wool board (65 mm), integer 6 is for the expanded polystyrene board (80 mm). T\({}_{\text{win}}\) refers to the window panel type, integer 0 under this column represents the double pane clear glass window and integer 3 represents the double silver low-e coating window. Table 7 illustrates that the performance of the relative optimal solutions was evidently better than that of the original design in all aspects. The EUI value was reduced by 5.1-6.7 kWh/m\({}^{2}\), which means that 1.6\(\times\)10\({}^{5}\)-2.1\(\times\)10\({}^{5}\) kWh energy could be saved per year. The indoor daylighting environment could be improved with an increase in sDA value by 8.1%-11.0% and an increase in UDI value by 4.3%-4.7%. Moreover, Building envelope cost (BEC) could be reduced by \(\lx@sectionsign\)1.2\(\times\)10\({}^{5}\)-2.1\(\times\)10\({}^{5}\) (\(\lx@sectionsign\)1.7\(\times\)10\({}^{4}\)-3.0\(\times\)10\({}^{4}\)). The whole optimization process just took 2 h with the implementation of ANN prediction models. Only 200 groups of energy and daylighting simulations were performed, the number can rise to 5000 groups in a traditional BPS based optimization process with the same population size and generation number, which will take much longer time to complete. Though the time for energy simulation modeling of a large-scale public building has not been shortened much, the way of energy simulation modeling in architectural parametric modeling software can be easier for architects to practice. Moreover, by integrating the whole process in the Rhino + Grasshopper platform, the efficiency was further improved when manual data conversion time was saved. Although Building Energy Simulation and Optimization is a research subject that has been extensively studied over the past two decades, it is not yet widely applied in the building design community [43]. This research hopes to encourage more widespread and effective usage of building many-objective optimization by architects. There is still a long way to go for not all architects have enough knowledge of building performance simulation and parametric modeling. However, more and more architects will want to learn the knowledge as the concept of zero-energy buildings and high-performance buildings is increasingly popular. The open source learning materials of Rhino + Grasshopper, as well as all kinds of Grasshopper plug-ins and building performance simulation software are enough for architects to master relevant skills gradually.