## 5 Results  
Comparison of energy consumption of the central heating system controlled by different optimization algorithms is shown in Table 1. The recorded measurement data clearly show variations in the performance of the different algorithms. By calculating the ratio of consumed thermal energy to the degree-hours in a period when a specific optimization algorithm was running, we can directly compare them. We see that Algorithm I outperforms Algorithms II and III in terms of energy consumption. The proposed method of normalization of energy consumption in relation to the outdoor temperature seems to be working, because values computed by (1) provide consistent results for each algorithm independently from the time of the year when the test took place. In the last two months, various algorithms were tested, so we did not assign data from this period to any algorithm. Comparison of underheating and overheating indices for different algorithms is shown in Table 2. The lower the values of \(E_{2}\) and \(E_{3}\), the better. Algorithms II and III are comparable. However, Algorithm II obviously overheats the building. The description of Algorithms I-III is a trade secret. For legal reasons, we cannot provide their description, nor can we provide the baseline energy consumption, i.e., what the performance of Algorithm 1 is, without adjusting the set point of the temperature of the central heating circuit supply water.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Month** & **Samples** & **Energy [kWh]** & \(\mathbf{T(t)}\) & **E\({}_{1}\) (I)** & **Algorithm** \\ \hline April, 2021 & 398 & 3565 & 3759 & 0.948 & I \\ May, 2021 & 495 & 7021 & 7069 & 0.993 & I \\ October, 2021 & 485 & 4373 & 4158 & 1.052 & II \\ November, 2021 & 385 & 5509 & 4818 & 1.143 & II \\ December, 2021 & 727 & 16,540 & 13,653 & 1.211 & III \\ January, 2022 & 744 & 15,145 & 12,638 & 1.198 & III \\ February, 2022 & 672 & 11,416 & 9789 & 1.166 & III \\ March, 2022 & 742 & 11,868 & 10,276 & 1.154 & III \\ April, 2022 & 720 & 7815 & 7105 & 1.100 & _Various_ \\ May, 2022 & 743 & 2479 & 2645 & 0.937 & _Various_ \\ \hline April–May, 2021 & 893 & 10,586 & 10,828 & 0.978 & I \\ October–November, 2021 & 870 & 9883 & 8976 & 1.101 & II \\ December–March, 2022 & 2885 & 54971 & 46,357 & 1.186 & III \\ \hline \hline \end{tabular}
\end{table}
Table 1: Changes in energy consumption in the test building with different optimization algorithms. \(T(t)\) denotes degree-hours.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Month** & **Samples** & \(t<21\) & **E\({}_{2}\) (I)** & \(t>21\) & **E\({}_{3}\) (I)** & **Algorithm** \\ \hline April, 2021 & 576 & 0 & 0 & 576 & 1.78 & I \\ May, 2021 & 456 & 31 & 0.02 & 425 & 1.19 & I \\ October, 2021 & 422 & 0 & 0 & 422 & 2.45 & II \\ November, 2021 & 133 & 0 & 0 & 133 & 1.38 & II \\ December, 2021 & 672 & 17 & 0 & 654 & 1.48 & III \\ January, 2022 & 696 & 0 & 0 & 696 & 1.79 & III \\ February, 2022 & 633 & 107 & 0.07 & 525 & 1.5 & III \\ March, 2022 & 671 & 0 & 0 & 671 & 1.69 & III \\ \hline April–May, 2021 & 516 & 15 & 0.01 & 501 & 1.52 & I \\ October–November, 2021 & 278 & 0 & 0 & 278 & 2.19 & II \\ December–March, 2022 & 668 & 30 & 0.02 & 638 & 1.62 & III \\ \hline \hline \end{tabular}
\end{table}
Table 2: Underheating and overheating indices in the test building during the test period.  
Apart from implementation details regarding computations made by optimization algorithms, we see that they indeed influence energy consumption while the system is still under supervision of the legacy controller, ensuring proper functioning of low-level mechanisms. The measurements show that there are differences in the algorithms' performance. However, determining what difference is considered to be significant, and then deciding which algorithm is better, requires additional research.