Algorithm 2. Optimization of (53) via CPSO

Input:${\tilde{\mathit{y}}}_s^{\ast },{\tilde{\mathit{A}}}_s^{\ast },{\mathit{x}}_s^{\ast },{\tilde{\mathit{e}}}_s^{\ast },{\eta }_0,\varsigma ,{\eta }_{\max },\xi ,Q$, and $S$

Output: The optimal ${\mathit{\lambda }}^{\ast }$

Initialization:$m=0$, particle swarm ${\mathit{P}}^m$

Repeat

1: Calculate the fitness value of each individual in ${\mathit{P}}^m$ on (53);

2: Find the individual ${\mathit{p}}^{\ast }$ in ${\mathit{P}}^m$ with least fitness value;

3: $\mathit{\lambda }={\mathit{p}}^{\ast }$;

4: $m=m+1$;

5: Reproduce particle swarm ${\mathit{P}}^m$ around ${\mathit{p}}^{\ast }$;

6: Update ${\eta }^m$ by (55);

7: Check the termination criterion by (54);

Until convergence