# Energy Demand and Supply Simultaneous Optimization to Design a Nearly Zero-Energy House
## 3 Results
### Financial Objective--Sequential Optimization and Energy Supply  
The second step of the sequential approach referred to energy supply optimization, entailing financial optimization of active design parameters (Table 3) when the passive ones were fixed to the optimal values resulting from the first step (minimization of energy demand). The optimization process ran in this second step led to evaluate almost 400 different design options, which were reported in the cost-optimal cloud in Figure 9. The profiles indicating optimal parameter values related to the cost-optimal point and to the other significant points are pictured in Figure 10.  
Figure 8: Robustness profile: window type, south; financial objective, sequential optimization. Figure 9: Cost-optimal cloud: financial objective, sequential optimization, energy supply. Concerning the solar thermal system, four evacuated tube collectors resulted as the cost-optimal design option, together with a water storage that had a volume of 600 L (ratio of 75 L/m\({}^{2}\)\({}_{\text{pan}}\)). The optimal slope for solar collectors was 45\({}^{\circ}\), which maximized their performances during the winter season. A greater area of PV panels was optimal, as eight was the optimal value for the related parameter (8 panels = 13 m\({}^{2}\)). The polycrystalline PV type was selected, given its superior peak production cost ratio. In this case, the resulting optimal slope was 30\({}^{\circ}\). Concerning the heating system, the reversible geothermal heat pump was optimal. This set of optimal values for active parameters, applied to the previously optimized building envelope, led to an overall primary energy consumption of 90.83 kWh\({}_{\text{EPtot}}\)/m\({}^{2}\). This was nearly 40% of the energy consumption calculated with the reference systems in the case of the building optimization thanks to the exploitation of renewable energies combined with a more efficient heat generator. Figure 10 provides insights into the way in which the algorithm explored the space of solutions. Each grey line linked the values that each design parameter assumed in one of the analyzed design options. All the design options investigated by the algorithm, shown as points in Figure 9, were represented, which allowed a quick comparison between the best solution and the others explored by the optimization algorithm. The optimal solution was shown by the green profile. Figure 11 reports all combinations of parameter values that were in the optimum neighborhood and helping visualize the robustness of the resulting optimal solution (red profile). Almost all solutions had the geothermal heat pump as the heat generator (about 99%) with the majority of them having the evacuated tube as the type of solar thermal collector (75%). Moreover, within this group of points there was a prevalence of solutions with a small number (four) of solar collectors. Similarly, the selected optimal type of PV panels was the most efficient one (polycrystalline silicon), whereas the optimal number of PV panels was an intermediate value (eight), which was selected by the algorithm in about 50% of the cases. Similar to Figure 8, Figure 12 reported the frequency of occurrence of each value for parameter \"number of PV panels\" within the optimization process and within the optimum neighborhood, quantifying the robustness of the resulting optimal value. Figure 10: Design configuration networks: financial objective, sequential optimization, energy supply. The entire set of resulting optimal parameter values and the related robustness is reported in the summary in Table 6.  
Figure 11: Design configuration networks: cost optimal neighborhood, sequential optimization, energy supply. Figure 12: Robustness profile: number of PV panels, financial objective, sequential optimization.