# Plum Tree Algorithm and Weighted Aggregated Ensembles for Energy Efficiency Estimation
## 4 Results
Table 5 presents the specific configurations of the nature-inspired algorithms used in the experiments. The configuration parameters of the PSO algorithm, the GWO, and the CS algorithm were the ones from the EvoloPy library, whereas those of the CSO algorithm, the CSA, and the HOA were taken from the original articles which introduced them. The configuration parameters of the PTA were selected after a series of in-house experiments. They were inspired by the configuration parameters of other nature-inspired \begin{table}
\begin{tabular}{c c c c} \hline
**Objective Function** & **Mathematical Formula** & **Range** & **N** & **Optimal Value** \\ \hline \(h_{7}\) & \(-\sum_{i=1}^{4}cexp\left(-\sum_{j=1}^{5}a_{ij}(x_{j}-p_{ij})^{2}\right)\) & \([0,1]\) & \(6\) & \(-3.32\) \\ \hline \(h_{8}\) & \(-\sum_{i=1}^{5}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & \([0,10]\) & \(4\) & \(-10.1532\) \\ \hline \(h_{9}\) & \(-\sum_{i=1}^{7}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & \([0,10]\) & \(4\) & \(-10.4029\) \\ \hline \(h_{10}\) & \(-\sum_{i=1}^{10}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & \([0,10]\) & \(4\) & \(-10.5364\) \\ \hline \end{tabular}
\end{table} 
Table 4: \(Cont.\) \begin{table}
\begin{tabular}{c c c} \hline
**Nature-Inspired Algorithm** & **Specific Configurations** & \\ \hline \hline \multirow{2}{*}{CSO} & **Parameter** & **Value** \\  & **Parameter** & **Value** \\ \hline \multirow{4}{*}{CSO} & hierarchical order update frequency (\(G\)) & \(10\) \\  & minimum flight length (\(FL_{min}\)) & \(0.5\) \\  & maximum flight length (\(FL_{max}\)) & \(0.9\) \\  & zero division avoiding constant (\(e\)) & \(1.0\times 10^{300}\) \\  & rosters percent (\(RP\)) & \(20\) \\  & hens percent (\(0\)) & \(60\) \\  & mother hens percent (\(MP\)) & \(10\) \\ \hline \multirow{4}{*}{PSO} & minimum velocity (\(V_{min}\)) & \(-6\) \\  & maximum velocity (\(V_{max}\)) & \(6\) \\  & minimum inertia (\(w_{min}\)) & \(0.2\) \\  & maximum inertia (\(w_{max}\)) & \(0.9\) \\  & cognitive component constant (\(c_{1}\)) & \(2\) \\  & social component constant (\(c_{2}\)) & \(2\) \\ \hline GWO & parameter \(a\) & \(2\) \\ \hline CS & discovery rate of alien eggs (\(p_{a}\)) & \(0.25\) \\ \hline CSA & flight length (\(fl\)) & \(2\) \\ \hline \multirow{4}{*}{HOA} & awareness probability (\(AP\)) & \(0.1\) \\  & reorganization frequency (\(M\)) & \(10\) \\  & dominant stallions percent (\(DSP\)) & \(10\) \\  & horse distribution rate (\(HDR\)) & \(10\) \\  & horse memory pool (\(HMP\)) & \(10\) \\  & single stallions percent (\(SSP\)) & \(10\) \\  & minimum velocity (\(V_{min}\)) & \(-0.1\) \\  & maximum velocity (\(V_{max}\)) & \(0.1\) \\  & standard deviation (\(sd\)) & \(1\) \\ \hline \multirow{4}{*}{PTA} & zero division avoiding constant (\(e\)) & \(1.0\times 10^{300}\) \\  & fruitiness threshold (\(FT\)) & \(0.8\) \\  & ripeness threshold (\(RT\)) & \(0.2\) \\  & minimum fruitiness rate (\(FR_{min}\)) & \(0.5\) \\  & maximum fruitiness rate (\(FR_{max}\)) & \(1\) \\ \hline \end{tabular}
\end{table} 
Table 5: Nature-Inspired Algorithms’ Specific Configurations. The PTA showed large variations for \(f_{3}\), \(h_{8}\), and \(h_{9}\). It also showed a larger deviation from the optimal solution in the case of these three objective functions. One of the reasons for this is represented by the values of the configuration parameters. The default values of the PTA configuration parameters were inspired by those used by the algorithms which were its sources of inspiration; this is why it returned overall good results with few exceptions. For example, when FT and RT were set to 0.5 and 0.3, respectively, the results for \(f_{3}\) are 10.76859 as the mean and 15.47429 as the standard deviation (std), the results for \(h_{8}\) are a mean of \(-10.1531\) and a std of 0.000252, and the results for \(h_{9}\) are a mean of \(-10.4027\) and a std of 0.044829.