## 3 Results  
### Experimental Setup  
The experiments in this study are performed on the GMPB test suite, the parameters are set equal to those in [10] and given in Table 1.  
There settings considered in this study were: a standard computational resource of 5000 function evaluations between changes, decreased to 2500 function evaluations; with the number of peaks increased to 25, and shift severities increased from 2 to 4. The settings are provided in Table 2.  
The following algorithms parameters were set for both mQSO and mQSDE algorithms:  
* Number of swarms \(N_{s}=10\) (independent of the number of components),
* Number of quantum points \(N_{q}=5\),
* \(w=0.7298\), \(c_{1}=2.05\) and \(c_{2}=2.05\),
* \(r_{cloud}=2\), \(r_{conv}=r_{excl}=0.5(Ub-Lb)/N_{s}^{d}\)
* Number of algorithm runs: 31. The number of individuals in each swarm \(N_{p}\), probability of applying differential mutation and binomial crossover \(P_{DE}\), type of mutation operator, \(mF\) and \(Cr\) were varied in the experiments: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Dimension & \(d\) & 10 \\ Shift severity & \(\widetilde{s}\) & 2, 4 \\ Number of components & \(m\) & 10, 25 \\ Angle severity & \(\widetilde{\theta}\) & \(\pi/9\) \\ Height severity & \(\widetilde{h}\) & 7 \\ Width severity & \(\widetilde{w}\) & 1 \\ Irregularity parameter \(\tau\) severity & \(\widetilde{x}\) & 0.05 \\ Irregularity parameter \(\eta\) severity & \(\widetilde{\eta}\) & 2 \\ Search range & \([Lb,Ub]^{d}\) & \([-50,50]^{d}\) \\ Height range & \([h_{min},h_{max}]\) & \([30,70]\) \\ Width range & \([w_{min},w_{max}]^{d}\) & \([1,12]^{d}\) \\ Angle range & \([\theta_{min},\theta_{max}]\) & \([-\pi,\pi]\) \\ Irregularity parameter \(\tau\) range & \([\tau_{min},\tau_{max}]\) & \([0,0.4]\) \\ Irregularity parameter \(\eta\) range & \([\eta_{min},\eta_{max}]\) & \([10,25]\) \\ Initial center position & \(c_{k}^{(0)}\) & \(U[Lb,Ub]^{d}\) \\ Initial height & \(h_{k}^{(0)}\) & \(U[h_{min},h_{max}]\) \\ Initial width & \(w_{k}^{(0)}\) & \(U[w_{min},w_{max}]^{d}\) \\ Initial angle & \(\theta_{k}^{(0)}\) & \(U[\theta_{min},\theta_{max}]\) \\ Initial irregularity parameter \(\tau\) & \(\tau_{k}^{(0)}\) & \(U[\tau_{min},\tau_{max}]\) \\ Initial irregularity parameter \(\eta\) & \(\eta_{k}^{(0)}\) & \(U[\eta_{min},\eta_{max}]^{d}\) \\ Initial rotation matrix & \(R_{k}^{(0)}\) & \(GS\big{(}Norm(0,1)^{d\times d}\big{)}\) \\ Change frequency & \(\widetilde{v}\) & 2500, 5000 \\ Number of Environments & \(T\) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The set of Generalized Moving Peaks Benchmark (GMPB) parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Symbol** & **Setting 1** & **Setting 2** & **Setting 3** & **Setting 4** \\ \hline Shift severities & \(\widetilde{s}\) & 2 & 4 & 2 & 2 \\ Numbers of components & \(m\) & 10 & 10 & 25 & 10 \\ Change frequency & \(\widetilde{v}\) & 5000 & 5000 & 5000 & 2500 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tested settings. \(N_{p}=\{5,9,13,17,21,25,29,33\}\)
* \(P_{DE}=\{0.1,0.2,0.3\}\)
* Type of mutation: based on current points and based on personal best
* \(mF=\{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1\}\)
* \(Cr=\{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1\}\)  
The tested variants further in the text are marked as mQSO\({}_{N_{p}}\), mQSODE\({}^{mF,Cr}_{N_{p},P_{DE},x}\) for mutation based on current positions, and mQSODE\({}^{mF,Cr}_{N_{p},P_{DE},p}\) for mutation based on personal best positions. If the upper indexes for mQSOE are missing, e.g., mQSODE\({}_{N_{p},P_{DE},x}\), then \(mF=0.3,Cr=1\). There were two performance indicators used in this study: \(E_{BCC}\), and \(E_{O}\).