## 4 Experiments
### Comparison with MFO  
To verify the performance of IMTO, optimization results of IMTO and MFO on test suites 1 and 2 are summarized. MTO algorithms are designed based on different single-task algorithms. This work compares IMGA with MFEA, IMDE with MFDE, and IMPSO with MFPSO. The computational time results of different algorithms are shown in Table 4 and Figure 3.  
It can be found that although IMGA, IMPSO, and IMDE need to finish information exchange in each generation, their running time is much shorter than MFO. For example, MFPSO needs 19.03s to optimize \(P_{2}\), while IMPSO just needs 3.43s in Table 4. This can also apply to IMGA and IMDE. IMTO prefers to maintain the vertical evolution of each task, and each generation just needs to evaluate objective functions and communicate information. However, MFEA, MFPSO, and MFDE need to divide task groups at each generation, and the calculations of factorial cost, factorial rank, scalar fitness, and skill factor consume many computation resources. Hence, the knowledge transfer scheme of IMTO is much more efficient than the method of multifactorial influence used in MFEA, MFPSO, and MFDE. +++ ==ERROR: No output for this page==
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Task Set**}} & \multicolumn{2}{c}{**IMGA**} & \multicolumn{2}{c}{**MFEA**} & \multicolumn{2}{c}{**IMPSO**} & \multicolumn{2}{c}{**MPPSO**} & \multicolumn{2}{c}{**IMODE**} & \multicolumn{2}{c}{**MFDE**} \\ \cline{2-13} \multicolumn{1}{c}{**Task Set**} & \multicolumn{2}{c}{**G-Based**} & \multicolumn{2}{c}{**FSO-Based**} & \multicolumn{2}{c}{**De-Based**} & \multicolumn{2}{c}{**De-Based**} \\ \cline{2-13} \cline{3-13}  & \multicolumn{2}{c}{**Fitness**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Fitness**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Fitness**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Fitness**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Fitness**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Fitness**} & \multicolumn{2}{c}{**Time**} \\ \hline \multirow{3}{*}{\(P_{1}\)} & \(T_{1}\) & \(11\times 10^{-1}\) & \(3.35\times 10^{-1}\) & & \(49\times 10^{-1}\) & & \(5.20\times 10^{-1}\) & & \(1.28\times 10^{-1}\) & & \(8.77\times 10^{-1}\) \\  & \(T_{2}\) & \((5.27\times 10^{-1})\) & \(4.02\) & \((6.85\times 10^{-1})\) & \(18.57\times 10^{-1}\) & \(49.5\times 10^{-1}\) & \(49.5\times 10^{-1}\) & \(49.5\times 10^{-1}\) & & \(16.26\times 10^{-1}\) & & \(21.79\times 10^{-1}\) \\  & \(T_{2}\) & \((3.39\times 10^{-1})\) & \(4.02\) & \((2.27\times 10^{-1})\) & \(18.57\times 10^{-1}\) & \(49.5\times 10^{-1}\) & \(3.49\times 10^{-1}\) & \(3.32\times 10^{-1}\) & \(21.79\times 10^{-1}\) & \((5.03\times 10^{-1})\) & \(4.87\times 10^{-1}\) & \((26.53\times 10^{-1})\) & \(20.29\times 10^{-1}\) \\  & \(T_{2}\) & \((47.2\times 10^{-1})\) & \((53\times 10^{-1})\) & & \(6.25\times 10^{-1}\) & & \((25.4\times 10^{-1})\) & & \((3.50\times 10^{-1})\) & & \((1.14\times 10^{-1})\) \\ \hline \multirow{3}{*}{\(P_{3}\)} & \(T_{1}\) & \(\mathbf{3.8\times 10^{1}}\) & & \(8.00\times 10^{-1}\) & & \(8.90\times 10^{-1}\) & & \(5.32\times 10^{-1}\) & & \(4.24\times 10^{-1}\) & & \(1.08\times 10^{-1}\) & \\  & \(T_{2}\) & \((3.85\times 10^{-1})\) & \(\mathbf{4.24}\) & \((6.85\times 10^{-1})\) & \(19.04\) & \((4.54\times 10^{-1})\) & \(\mathbf{3.4}\) & \(6.88\times 10^{-1}\) & \(19.03\) & \((5.45\times 10^{-1})\) & \(\mathbf{5.47}\times 10^{-1}\) & \(\mathbf{1 To better show effects of knowledge transfer on solution accuracy, the optimization results of IMTO and MFO on test suites 1 and 2 are summarized in Tables 4 and 5. The mean and standard deviation of the best achieved fitness values obtained via 20 independent runs are presented. The best performance of fitness values is shown in bold. It is obvious that the proposed IMTO exhibits a better overall performance than its peer, i.e., MFO.