## 3 Results
### Results of Computational Experiments
This means that switching the main search mechanism to DE is not desirable for dynamic environments, and the application of DE should be assisting PSO, but not replacing it. It is also important to mention that the best results for the case of \(P_{DE}=0.2\) were achieved with a smaller number of particles than with \(P_{DE}=0.1\), which means that more often applications of DE increase the diversity of individual swarms so that smaller swarm sizes are sufficient. The sensitivity of mQSODE to crossover rates and scaling factor values were tested and obtained results are demonstrated in Tables 6 and 7. The comparison of performance metric values in Tables 6 and 7 shows that DE search parameters do not have a significant influence on the final performance, however, the influence of scaling factor sampling parameter \(mF\) is larger than the influence of crossover rate \(Cr\). The best performing configuration here is mQSODE\({}^{0.3,1.0}_{21,0.1,p}\). \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 mQSODE\({}_{5,0,2,p}\) & \(18.16\pm 2.43\) & \(22.01\pm 2.61\) & \(23.83\pm 3.25\) & \(30.06\pm 3.42\) \\ mQSODE\({}_{9,0,2,p}\) & \(10.41\pm 1.81\) & \(14.15\pm 2.10\) & \(14.23\pm 1.71\) & \(20.02\pm 1.72\) \\ mQSODE\({}_{13,0,2,p}\) & \(\mathbf{8.75}\pm\mathbf{1.08}\) & \(\mathbf{12.25}\pm\mathbf{1.21}\) & \(13.06\pm 1.33\) & \(18.72\pm 1.43\) \\ mQSODE\({}_{17,0,2,p}\) & \(8.82\pm 1.79\) & \(12.41\pm 1.91\) & \(\mathbf{13.01}\pm\mathbf{1.43}\) & \(\mathbf{18.57}\pm\mathbf{1.53}\) \\ mQSODE\({}_{21,0,2,p}\) & \(9.13\pm 1.37\) & \(12.80\pm 1.52\) & \(13.23\pm 1.25\) & \(18.82\pm 1.53\) \\ mQSODE\({}_{25,0,2,p}\) & \(8.82\pm 0.82\) & \(12.35\pm 1.06\) & \(13.85\pm 1.35\) & \(19.35\pm 1.57\) \\ mQSODE\({}_{29,0,2,p}\) & \(9.36\pm 1.12\) & \(12.93\pm 1.29\) & \(14.09\pm 1.27\) & \(19.42\pm 1.45\) \\ mQSODE\({}_{33,0,2,p}\) & \(9.81\pm 1.36\) & \(13.49\pm 1.46\) & \(14.57\pm 0.97\) & \(19.99\pm 1.17\) \\ mQSODE\({}_{5,0,3,p}\) & \(19.80\pm 3.94\) & \(24.01\pm 4.40\) & \(25.93\pm 4.16\) & \(32.53\pm 4.37\) \\ mQSODE\({}_{9,0,3,p}\) & \(10.78\pm 1.73\) & \(14.68\pm 1.84\) & \(15.31\pm 2.51\) & \(21.45\pm 2.70\) \\ mQSODE\({}_{13,0,3,p}\) & \(9.51\pm 1.50\) & \(13.14\pm 1.70\) & \(13.62\pm 1.63\) & \(19.48\pm 1.74\) \\ mQSODE\({}_{17,0,3,p}\) & \(8.97\pm 1.17\) & \(12.56\pm 1.31\) & \(13.83\pm 1.26\) & \(19.57\pm 1.45\) \\ mQSODE\({}_{21,0,3,p}\) & \(9.25\pm 1.38\) & \(12.89\pm 1.54\) & \(14.05\pm 1.46\) & \(19.62\pm 1.72\) \\ mQSODE\({}_{25,0,3,p}\) & \(9.45\pm 0.97\) & \(13.13\pm 1.23\) & \(14.38\pm 1.03\) & \(19.91\pm 1.16\) \\ mQSODE\({}_{9,0,3,p}\) & \(9.66\pm 0.93\) & \(13.31\pm 1.09\) & \(14.95\pm 1.09\) & \(20.29\pm 1.19\) \\ mQSODE\({}_{33,0,3,p}\) & \(10.34\pm 1.17\) & \(13.93\pm 1.30\) & \(15.25\pm 1.44\) & \(20.88\pm 1.71\) \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{Setting 3} & \multicolumn{2}{c}{Setting 4} \\  & \(E_{BBC}\) & \(E_{O}\) & \(E_{BBC}\) & \(E_{O}\) \\ \hline mQSODE\({}_{5,0,2,p}\) & \(18.76\pm 2.64\) & \(22.54\pm 2.74\) & \(21.69\pm 3.12\) & \(26.17\pm 3.25\) \\ mQSODE\({}_{9,0,2,p}\) & \(10.95\pm 1.40\) & \(14.44\pm 1.42\) & \(14.40\pm 1.72\) & \(18.90\pm  
Table 8 contains the comparison of two tested algorithms in this study, mQSO\({}_{29}\) and mQSO\({}_{21,0.1,p}\) with alternative approaches on the same benchmark. Table 8 shows that although the mQSDDE\({}_{21,0.1,p}\) is not capable of outperforming some of the alternative methods, it is still highly efficient compared to PSO-based algorithms, such as FTmPSO and mPSO. In particular, it achieves better results in terms of offline error \(E_{O}\) especially for more challenging settings 3 and 4. It should be noted that unlike the algorithms from [10], in this study the shift severity learning was not performed, and the shift severity value was set to 2, which is used by quantum particles.