## 4 Experiments
### Experimental Setup  
In order to show the knowledge transfer effects of different kinds of MTO algorithms, we use two test suites of test problems in our experiments. Test suite 1 contains 9 composite two-task problems used in CEC 2017 EMTO Competition [50]. These nine problems belong to nine categories with different degrees of overlap and different degrees of inter-task similarity. It uses CI, PI, and NI to represent complete, partial, and no intersection, and HS, MS, and LS to mean high, medium, and low similarity, respectively. Details of test problems are given in Table 1. \(T_{1}\) and \(T_{2}\) denote two component tasks of each multi-task optimization problem. The second test suite of the CEC2021 EMTO Competition consists of much more complex objective functions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Task Set** & **Category** & **Task Component** & **Dimensionality** & **Search Space** &
\begin{tabular}{c} **Inter-Task Similarity** \\ \end{tabular} \\ \hline \multirow{2}{*}{\(P_{1}\)} & \multirow{2}{*}{CI+HS} & [PERSON] (\(T_{1}\)) & 50 & \([-100,100]\) & \multirow{2}{*}{1.00} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-50,50]\) & \\ \hline \multirow{2}{*}{\(P_{2}\)} & \multirow{2}{*}{CI+MS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.22} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-50,50]\) & \\ \hline \multirow{2}{*}{\(P_{3}\)} & \multirow{2}{*}{CI+LS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.00} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-500,500]\) & \\ \hline \multirow{2}{*}{\(P_{4}\)} & \multirow{2}{*}{PI+HS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.86} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-100,100]\) & \\ \hline \multirow{2}{*}{\(P_{5}\)} & \multirow{2}{*}{PI+MS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.21} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-50,50]\) & \\ \hline \multirow{2}{*}{\(P_{6}\)} & \multirow{2}{*}{PI+LS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.07} \\  & & [PERSON] (\(T_{2}\)) & 25 & \([-0.5,0.5]\) & \\ \hline \multirow{2}{*}{\(P_{7}\)} & \multirow{2}{*}{NI+HS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.94} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-50,50]\) & \\ \hline \multirow{2}{*}{\(P_{8}\)} & \multirow{2}{*}{NI+MS} & [PERSON] (\(T_{1}\)) & 50 & \([-100,100]\) & \multirow{2}{*}{0.36} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-0.5,0.5]\) & \\ \hline \multirow{2}{*}{\(P_{9}\)} & \multirow{2}{*}{NI+LS} & [PERSON] (\(T_{1}\)) & 50 & \([-50,50]\) & \multirow{2}{*}{0.00} \\  & & [PERSON] (\(T_{2}\)) & 50 & \([-500,500]\) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of properties of problem pairs in test suite 1.  
The initial population size is set to 100, and each task is assigned with 50 individuals. In MFEA, the distribution index for crossover \(\eta_{C}\) is set as 10. Acceleration coefficients of MFPSO are set to 0.2. The weight of IMPSO and MFPSO decreases linearly from 0.9 to 0.4. In IMABC, the number of omlooker bees is set as 50. The value of random mating probability controls knowledge transfer in a multi-task paradigm, and in MFEA, MFPSO, and MFDE, we set rmp to 0.3 in all experiments by following [21,33]. We set individual learning \(p\_\)_il_ of MFEA, MFDE, and MFPSO to 0. The sensitivities of \(\Omega\) and \(\gamma\) are to be discussed later.  
Other parameters used in this work are summarized as: (1) Maximum number of generations: \(\hat{g}=1000\); (2) Independent number of runs: \(\hat{r}=20\).  
We choose parallel GAs, PSOs, DEs, and ABCs as four baseline solvers, named as B-GA, B-PSO, B-DE, and B-ABC, respectively. All the baseline solvers share the same parameters and search operators of IMGA, IMPSO, IMDE, and IMABC to guarantee fair comparisons. Experiments are conducted by using the computer with a 1.00 GHz Intel Corei5 processor and 16 GB RAM under window10.