Open Access

Table A1

Pseudo code of the CIMPSO algorithm [31].

Input: Learning factor c 1,c 2; Particle swarm size N; Number of iterations T; Velocity inertia weight w u ; Position inertia weight w x ; Expansion factorsα and β; Control parameter μ; Chaotic variable element numbering c.
Initialization: The position of the particles ;
//j is the number of the particle element.
1. For n = 1 to T
2. For m = i to N
3. Characteristic number of nonlinear element ;
  //i is Number of the particles.
4. Generate chaotic variables ;
  //t is the number of iteration steps.
5. ;
// Chaotic variable element assignment.
6. Evaluate the fitness of :, and ;
7. Update the locally optimal particle: , and;
8. End For
9. Perform non-dominated sorting on the local optimal particle
  fitness to get the first dominated layer particle P (t);
10. Global optimal particle P g  (t+1) = maxfit [P d  (t)];
  //maxfit (⋅) represents the particle with the optimal fitness.
11. ; //Chaos (.) represents chaotic map.
12. ;
// The particles with the worst fitness are replaced.
13. ;
  //worst represents the subscript of the worst-fit particle.
14. V i  (t + 1) = w v V i  (t) + c 1 r 1 [P i  (t) − X i  (t)] + c 2 r 2 [P g  (t) − X i  (t)];
  // Update particle velocity.
15. X i  (t + 1) = w x X i  (t) + V i  (t + 1); // Update particle position.
16. End For
17. Output: Non-inferior optimal solution set P g  (t).

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