## 4 Experiments
### Comparison with Baseline Solvers  
This section compares IMTO with baseline solvers to further illustrate its generality. Table 6 shows the mean and standard deviation of the best achieved fitness values obtained via 20 independent runs on test suite 1. The best fitness values are shown in bold.  
It can be found that even though baseline solvers have different characteristics, IMTO always has superior optimization performance over traditional baseline solvers. The performance superiority of IMTO over baseline solvers can be evidenced by the fact that IMGA significantly outperforms B-GA in 17 out of 18 tasks, IMPSO outperforms B-PSO in 14 out of 18 tasks, IMDE outperforms B-DE in 13 out of 18 tasks, and IMABC outperforms B-ABC in 15 out of 18 tasks on test suite 1. The individually guided learning and archive-memory schemes of IMTO share useful optimization experience in the unified search space, and update inferior individuals continuously through learning from better-performing individuals of other tasks.  
Solving tasks with low similarities shows higher challenges for MTO. The results in Table 6 show that IMGA achieves higher better optimization accuracy than B-GA in most cases. The knowledge transfer scheme can help the algorithms find globally optimal solutions for problems possessing different properties. The \(P_{6}\)-\(T_{1}\) optimization result shows that the baseline solver GA just finds the fitness value of 1.47e+01, but IMGA can find the value of 3.74e+00 by sharing historical experience. Similarly, IMPSO, IMDE, and IMABC perform better in most cases than PSO, DE, and ABC according to Table 6. In IMTO, the superior individuals need not learn from other tasks, which can maintain the vertical evolution of each task. Compared with a single-task solver, inferior individuals can constantly learn from other tasks to avoid being trapped into local optima, thereby suppressing negative transfer.  
The convergence curve of \(P_{5}\) in 1000 iterations is shown in Figure 5. It can be easily found that IMTO has faster convergence in most cases. IMTO's additional horizontal evolution allows for the exchange of information among different tasks. Different task groups are located in homogenous search spaces, and assisted tasks can provide useful knowledge, thereby speeding up the algorithms' convergence.  
Figure 4: Convergence traces of IMTO and MFO on multitasking problem \(P_{5}\) in test suite 1. (**a**) Convergence traces of IMGA and MFEA, (**b**) Convergence traces of IMPSO and MFPSO, and (**c**) Convergence traces of IMDE and MFDE.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Task Set**} & \multicolumn{2}{c}{**IMCA**} & \multicolumn{2}{c}{**GA**} & \multicolumn{2}{c}{**MODE**} & \multicolumn{2}{c}{**DE**} & \multicolumn{2}{c}{**IMPSO**} & \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**IMARC**} & \multicolumn{2}{c}{**ADC**} \\ \cline{3-10} \multicolumn{1}{c}{} & \multicolumn{1}{c}{**CA-Based**} & \multicolumn{1}{c}{**DE-Based**} & \multicolumn{1}{c}{**PSO-Based**} & \multicolumn{1}{c}{**ABC-Based**} \\ \hline \multirow{2}{*}{\(P_{1}\)} & \(T_{1}\) & \(1.11\times 10^{-1}\) & \(92.22\times 10^{-1}\) & \(1.20\