Algorithm 1 SRPSMTO.

Input:

n (population size)

k (number of tasks)

$w,c_1,c_2$ (PSO parameters)

Output:

$\{{\mathit{x}}_1^{*},{\mathit{x}}_2^{*},\dots ,{\mathit{x}}_k^{*}\}$ (the best solution achieved on each of the k component tasks)

1:    Randomly generate a population $pop$ of size n.

2:   Evenly separate $pop$ into k subgroups and evaluate each subgroup on one corresponding task.

3:   Update the ${\mathit{pbest}}_i,i=1,\dots ,n$ and ${\mathit{gbest}}_j,j=1,\dots ,k$, and the ability vector ${\mathbf{\varphi }}_i={\left\{{\varphi }_{i,j}\right\}}_{j=1}^k$ of individual $p_i$ in $pop$.

4:   while (stopping conditions are not satisfied) do

5:     Update positions (see Equation (2)).

6:     Update velocities (see Algorithm 2 and 3).

7:     Evaluate all individuals and Update the ${\mathit{pbest}}_i,i=1,\dots ,n$ and ${\mathit{gbest}}_j,j=1,\dots ,k$ (see Algorithm 4).

8:      Update the ability vector of every individual.

9:  end while