## 5 Attained Results and Discussion
### Thermal Behaviour Improvements Using PCM: Melting Temperature Value Optimisation (Step 2)  
The strategy of this step starts with the use of PCM incorporated into the walls and ceiling in thermal zones TZ7 and TZ8. PCM was considered to be applied behind the double plasterboard for both constructive solutions (walls and ceiling). Then, an evolutionary algorithm to operate the EnergyPlus software in the model definition was used for performance assessment of the different solutions incorporating PCM. This evolutionary algorithm is based on the CMA-ES (covariance matrix adaptation evolution strategies) and HDE (hybrid differential evolution) that operates in series, repeating a sequence of generations for each algorithm until the objective function is achieved [50; 51]. The goal of this step is the PCM melting temperature value optimisation, combined with the ventilation parameters, using continuous and discrete variables in the optimisation process (see Table 2). The nomenclature used for the discrete variables, named by BioPCM(r) 'M\({}_{\text{a}}\)/Q\({}_{\text{b}}\)-c', are:  
* --Manufacturer's internal code for product identification, related to the thermal storage capacity of the material;
* --Manufacturer's internal code for phase change temperature of the product, where b is the phase change temperature value in \({}^{\circ}\)C;
* --Thickness of the manufacturer's product, in m.  
Natural ventilation through window opening was computed by the EnergyPlus algorithm depending on the infiltration level, openings aperture and wind intensity and direction. The optimisation process was run using heating demand and overheating rate as the objective functions to be minimised. Overheating was estimated considering an upper limit of 26 \({}^{\circ}\)C and using the Energy Management System (EMS) feature in EnergyPlus to program new outputs. With this optimisation, higher reductions in the overheating rate and a significant reduction in annual heating demand were achieved, when compared to the reference solution. The results observed in Figure 5 contain the Pareto front [52; 53], composed of points that are not strictly dominated by any other (black triangles), which represent a set of optimal solutions. The improvement attained concerning the overheating rate and heating demand reductions is remarkable compared with the reference model. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**List of Continuous Variables**} \\ \hline
**Parameter id. ** & **Description** & **Limits and Constraints** \\ \hline a0–a7 & \begin{tabular}{c} Ventilation system by thermal zone (h\({}^{-1}\)) \\ \end{tabular}  & \begin{tabular}{c} [0.3; 1.0] \\ \end{tabular}  \\ \hline \multicolumn{3}{c}{**List of Discrete Variables**} \\ \hline a8 & \begin{tabular}{c} Vindows opening \\ \end{tabular}  & \
\begin{tabular}{c} M\({}_{27}\)/Q\({}_{21}\)\_0.011 M\({}_{27}\)/Q\({}_{23}\)\_0.011 \\ M\({}_{27}\)/Q\({}_{27}\)\_0.011 M\({}_{27}\)/Q\({}_{25}\)\_0.011 \\ M\({}_{51}\)/Q\({}_{21}\)\_0.021 M\({}_{51}\)/Q\({}_{23}\)\_0.021 \\ BioPCM® &
\begin{tabular}{c} M\({}_{51}\)/Q\({}_{25}\)\_0.021 M\({}_{51}\)/Q\({}_{27}\)\_0.021 \\ M\({}_{91}\)/Q\({}_{21}\)\_0.037 M\({}_{91}\)/Q\({}_{23}\)\_0.037 \\ M\({}_{91}\)/Q\({}_{25}\)\_0.037 M\({}_{91}\)/Q\({}_{27}\)\_0.037 \\ \end{tabFrom the set of optimal solutions, three scenarios were chosen according to the following premises: 1--the minimum value of the heating demand; 2--the minimum value of the overheating rate; 3--balanced/trade-off solution between both objective functions (heating demand and overheating rate). For scenario 2, a melting temperature value below the upper limit of thermal comfort (26 \({}^{\circ}\)C), combined with the higher ventilation rate, was chosen. Concerning the heating demand, a reduction was attained with the PCM optimised to a melting temperature value of 23 \({}^{\circ}\)C along with a lower ventilation rate.