## 4 Results and Discussion  
The use of the methodology proposed in this article has made it possible to bring the optimal solution closer with each iterative step. This has been possible by reducing the search sample of independent variables of the optimization problem. As a result, the total number of simulations performed was 934, while the possible combinations were 531,441. Only 0.18% of cases had to be simulated, thus, significant computational time was saved. The solution reached improves the two optimization variables: the total heating demand of the building and the standard deviation from the heating demands of the individual dwellings. Thus, the optimal solution has a total heating demand of the building of 18.70 kWh/m\({}^{2}\)-year, while the initial situation was 55.24 kWh/m\({}^{2}\)-year (66% saving). In addition, the final standard deviation is 3.30, compared to its initial value of 9.77 (a reduction of 66%). Therefore, it has been possible to reduce the building's heating demands, especially where it was most needed, placing all the dwellings of the building in almost zero energy consumption levels for heating with the minimum necessary interventions to its envelope. Figure 7 shows all the simulated cases throughout the optimization procedure, representing the standard deviation versus the total heating demand of the building. This type of representation makes it possible to observe the so-called Pareto Front, with the cases located in its proximity being those of less standard deviation for each specific total heating demand of the building. Following the methodology described above, the solution was reached after four iterations. In this figure, the simulation cases of the first iteration are represented with grey squares, the cases of the second iteration with red triangles, the third iteration with green circles, and finally the fourth iteration with blue crosses. Additionally, cases that would be obtained if the entire building had the same level of insulation and type of windows have also been represented in the same figure with black rhombuses. A different Pareto Front corresponding to these cases with the same level of  
Figure 7: Pareto Front and simulated cases from the 1 st to 4 th iteration and for same insulation assumption. insulation has been represented with a black dotted line. Comparing both Pareto Front lines, it is observed that for equal demand for total heating of the building, the standard deviation would be much greater for the cases with the same insulation level, resulting in some dwellings having a very low demand, while in others it would be very high. The original case (no insulation) is labelled \"1\", the case with minimum insulation is labelled \"2\", the case with maximum insulation level is labelled \"3\", and the optimal case has label \"4\". To show the benefits of the proposed methodology in more detail for finding the optimum case, Figure 8 shows a zoomed display of the area of interest in Figure 7. It shows how the four iterations gradually approached the optimal solution. At the same time the number of simulation cases is smaller for each iteration. In the first iteration the number of simulated cases were 730, in the second iteration the simulated cases were 149, in the third iteration 40 cases, and finally in the fourth iteration only 15 cases were needed. In short, to compare the four most interesting cases, the building heating demand and the standard deviation are shown in Table 4 and Figure 9. As can be seen, with the maximum insulation level it is possible to achieve the lowest heating demand of the building but the standard deviation is higher than that of the optimum case. In this optimum case, the heating demand of the building is low enough to consider that the entire building can be considered a NZEB according to the Spanish regulation, which establishes a maximum value of 25 kWh/m\({}^{2}\cdot\)year for the A3 climate zone where the city of Cadiz is located [30]. This optimum case minimizes the disparities among all of the dwellings.