## 4 Experiments
### Comparison with MFO
To judge whether there is a significant difference among IMTO and its peers, [PERSON]'s rank-sum test at the significant level of 0.05 is invoked. Symbols \"\(-\)\" and \"\(+\)\" denote that the compared MFO algorithm performs significantly better and significantly worse than IMTO, while \"\(\approx\)\" indicates there is no statistically significant difference between them. The performance superiority of IMTO over MFO can be evidenced by the fact that IMGA significantly outperforms MFAE in 11 out of 18 tasks, IMPSO outperforms MFPSO in 13 out of 18 tasks, and IMDE outperforms MFDE in 7 out of 18 tasks on test suite 1. Table 5 shows that the optimization accuracy of IMTO and MFO are relatively similar on complex problems, but the computation time results in Figure 3 show that IMTO can greatly shorten the running time. For example, MFPSO needs 228.1 s to optimize \(P_{7}\), while IMPSO just needs 26.5 s. IMTO allows individuals to belong to different tasks as long as it shows higher skill membership values, which promotes the individuals' potential in task-solving. Besides, the superior individuals of assisted tasks can be used for providing knowledge to guide the evolution of target tasks, which can improve the optimization results. It is worth noting that all the results are shown in scientific notation, which means that presented results are limited by the precision. Even though some comparative results shown in Table 4 are nearly the same because of the precision limitation, their actual average best fitness values may be very different. When executing the [PERSON]'s rank-sum test, there is a significant difference between these comparative results. The convergence curves of IMTO and MFO in 1000 iterations are illustrated in Figure 4, and they can tell the search efficiencies of different algorithms. Each sub-figure shows the optimization processes of \(T_{1}\) and \(T_{2}\). \(Y\)-axis represents the fitness curves and \(X\)-axis denotes the number of generations. This work just shows the convergence trace of \(P_{5}\) due to page limitation. It can be easily found that IMTO possesses faster convergence than MFO. This is because shared archives can generate similar genetic materials, and IMGA, IMPSO, and IMDE can update the evolution direction of worse-performing individuals. Obviously, the more similar tasks, the greater optimization facilitation. MFEA, MFPSO, and MFDE control knowledge transfer through the rmp value and neglect task similarities, thus easily causing negative optimization transfer. So, the convergences of MFAE and MFPSO are slower than IMTO's. Figure 3: Comparison of six algorithms in terms of the average computational time (s) via 20 runs in test suite 2. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Task Set**} & \multicolumn{1}{c}{**IMCA**} & \multicolumn{1}{c}{**MPFA**} & \multicolumn{1}{c}{**IMPO**} & \multicolumn{1}{c}{**MPPSO**} & \multicolumn{1}{c}{**MPPSO**} & \multicolumn{1}{c}{**IMODE**} & \multicolumn{1}{c}{**MPDE**} \\ \hline \multicolumn{1}{c}{**F0-Based**} & \multicolumn{1}{c}{**DE-Based**} & \multicolumn{1}{c}{**DE-Based**} & \multicolumn{1}{c}{**DE-Based**} \\ \hline \(P_{1}\) & \(\frac{1}{T_{2}}\) & \(6.228\times 10^{2}\) (\(1.999\times 10^{2}\)) & \(6.241\times 10^{2}\)