Algorithm 1 Particle Swarm Optimization (PSO)

1:Initialize population ${\mathbf{X}}^{\left(0\right)}$ within the search space.   2:Initialize particle velocities ${\mathbf{V}}^{\left(0\right)}$.   3:Evaluate $f\left(x_i^{\left(0\right)}\right)$ for all particles.   4:Set ${\mathit{pbest}}_i=x_i^{\left(0\right)}$.   5:Set $\mathit{gbest}$ as the best ${\mathit{pbest}}_i$.   6:Compute ${\mathbf{v}}_{max}$ according to Equation (12).   7:while $t<T$ do   8:      for $i=1$ to N do   9:        Generate random vectors ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$. 10:        Update velocity according to Equation (11). 11:        Limit velocity components within $[-{\mathbf{v}}_{max},{\mathbf{v}}_{max}]$. 12:        Update position according to Equation (13). 13:        Project position into the feasible search space. 14:        Evaluate $f\left(x_i^{(t+1)}\right)$. 15:        if $f\left(x_i^{(t+1)}\right)$ improves $f\left({\mathit{pbest}}_i\right)$ then 16:           Update ${\mathit{pbest}}_i$. 17:        end if 18:        if $f\left({\mathit{pbest}}_i\right)$ improves $f\left(\mathit{gbest}\right)$ then 19:           Update $\mathit{gbest}$. 20:        end if 21:    end for 22:    $t=t+1$. 23:end while 24:return $\mathit{gbest}$.