## 3 Results
### Results of Computational Experiments  
In the first series of experiments, the influence of the population size on the performance of the mQSO algorithm is determined. In Table 3 the mean and standard deviations of the performance indicators are shown. The best results in Tables 3-9 are highlighted in bold case. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Setting 1**} & \multicolumn{2}{c}{**Setting 2**} \\  & \(E_{BBC}\) & \(E_{O}\) & \(E_{BBC}\) & \(E_{O}\) \\ \hline mQSO\({}_{5}\) & 25.53 \(\pm\) 5.54 & 29.72 \(\pm\) 5.94 & 32.67 \(\pm\) 5.39 & 39.09 \(\pm\) 5.67 \\ mQSO\({}_{9}\) & 14.29 \(\pm\) 3.07 & 18.05 \(\pm\) 3.18 & 17.97 \(\pm\) 3.53 & 24.11 \(\pm\) 3.60 \\ mQSO\({}_{13}\) & 11.71 \(\pm\) 1.89 & 15.47 \(\pm\) 1.98 & 15.22 \(\pm\) 2.67 & 21.27 \(\pm\) 2.80 \\ mQSO\({}_{17}\) & 10.16 \(\pm\) 1.81 & 14.03 \(\pm\) 1.94 & 13.30 \(\pm\) 2.25 & 19.38 \(\pm\) 2.46 \\ mQSO\({}_{21}\) & 9.40 \(\pm\) 2.21 & 13.18 \(\pm\) 2.21 & 12.60 \(\pm\) 1.52 & 18.60 \(\pm\) 1.71 \\ mQSO\({}_{25}\) & 9.12 \(\pm\) 1.58 & 13.13 \(\pm\) 1.77 & **12.31 \(\pm\) 1.60** & **18.47 \(\pm\) 1.75** \\ mQSO\({}_{29}\) & 9.00 \(\pm\) 1.64 & 12.99 \(\pm\) 1.76 & 12.66 \(\pm\) 1.90 & 18.85 \(\pm\) 2.19 \\ mQSO\({}_{33}\) & **8.70 \(\pm\) 1.29** & **12.76 \(\pm\) 1.43** & 12.55 \(\pm\) 1.50 & 18.86 \(\pm\) 1.68 \\ \hline \multirow{2}{*}{Algorithm} & \multicolumn{2}{c}{Setting 3} & \multicolumn{2}{c}{Setting 4} \\  & \(E_{BBC}\) & \(E_{O}\) & \(E_{BBC}\) & \(E_{O}\) \\ \hline mQSO\({}_{5}\) & 24.36 \(\pm\) 3.40 & 28.09 \(\pm\) 3.68 & 27.21 \(\pm\) 5.82 & 31.86 \(\pm\) 6.23 \\ mQSO\({}_{9}\) & 14.22 \(\pm\) 1.97 & 17.68 \(\pm\) 2.08 & 16.96 \(\pm\) 2.84 & 21.34 \(\pm\) 2.99 \\ mQSO\({}_{13}\) & 11.83 \(\pm\) 1.34 & 15.31 \(\pm\) 1.41 & 14.42 \(\pm\) 2.18 & 18.83 \(\pm\) 2.36 \\ mQSO\({}_{17}\) & 10.43 \(\pm\) 1.21 & 13.95 \(\pm\) 1.26 & 13.71 \(\pm\) 2.06 & 18.39 \(\pm\) 2.43 \\ mQSO\({}_{21}\) & 10.06 \(\pm\) 1.28 & 13.54 \(\pm\) 1.35 & 13.65 \(\pm\) 2.00 & 18.33 \(\pm\) 2.33 \\ mQSO\({}_{25}\) & 9.57 \(\pm\) 1.17 & 13.19 \(\pm\) 1.24 & 13.34 \(\pm\) 1.63 & **18.08 \(\pm\) 2.17** \\ mQSO\({}_{29}\) & **9.26 \(\pm\) 1.13** & **12.89 \(\pm\) 1.29** & **13.20 \(\pm\) 1.45** & 18.41 \(\pm\) 2.06 \\ mQSO\({}_{33}\) & 9.38 \(\pm\) 1.02 & 13.14 \(\pm\) 1.11 & 14.11 \(\pm\) 1.55 & 19.11 \(\pm\) 1.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of mQSO with different population sizes. As can be seen from Table 3, the GMPB test suite seems to favor larger population sizes, i.e., the best results were achieved with more than 20 individuals in each of the swarms. The reason for this could be that, unlike MPB, GMPB generates more complex terrains of the goal function after every change, and larger populations with increased diversity are able to locate better local optima. The best results were achieved by mQSO\({}_{29}\). In Table 4, the mQSODE algorithm is tested with \(P_{DE}=0.1\) and two different types of mutation: using current and personal best positions of each particle. The obtained results shown in Table 4 demonstrate that using the personal best positions of each particle instead of the current position allows for achieving significantly better results across different population sizes. The reason for such behavior could be that the current positions of particles are changing with every iteration, while personal best positions are rather fixed and contain some important information about the problem at hand, such as the location of local optima. Utilizing this information with differential search operators  
Table 5 contains the comparison of mQSODE with increased \(P_{DE}\) probabilities, the personal best positions are used in mutation. The results in Table 5 show that increasing the probability of using the DE search operator decreases the performance of mQSODE, and \(P_{DE}=0.3\) is worse than \(P_{DE}=0.2\) and, compared to Table 4, \(P_{DE}=0.2\) is worse than \(P_{DE}=0.1\).