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Table 2

Pseudo code of mMQHOA.

1. Input: Ac // Scale convergence accuracy
2. Initialization: k; //Number of particles; Initial scale
X ; κ k ; σ k //Particle swarm; Energy level scale; Pre-evolutionary scale
3. while(σ s  > A c )
4. While(σ k  > σ s )
5. While(Δ σ k  > σ s and )
6. σ k  = std (X) // Pre-evolutionary standard deviations
7. κ k  = std (F) // Standard deviations of objective functions
8. For each x i , //Generate sub particle swarm
9. R= INSA (x i ,) //Non-dominated sorting
10. Update x i  = x min(R) //R, Particle rank vector
12. // Post-evolutionary standard deviations
13. // Standard deviations of objective functions
14. ;
15. end
16. R= INSA(X) //Non-dominated sorting
17. Energy level reduction x mean  = x max(R) //R, Particle rank vector
18. end
19. σ s  = 0.5σ s //Scale reduction
20. end
21. Output: Particle swarm X ; Objective function matrix F (x i )

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