Table 1

Pseudocode of the modified particle swarm optimisation (PSO) algorithm with a restart strategy

Algorithm 1 Modified PSO with a restart strategy
1: P←INITIALIZE(pSize)

  • Initial particles (P)

2: for each particle in P  
3: v←INITIALIZE_V()

  • Initial particle’s velocity

4: p←INITIALIZE_P()

  • Initial particle’s position

5: pbest←INITIALIZE_PB()

  • Initial particle’s pbest (denotes the individual optimum)

6: gbest←INITIALIZE_GB()

  • Initial gbest (denotes the global optimum by a global structure)

7: fitnessgbest ←COMPUTEFITNESS(gbest)

  • Compute global fitness

8: count←0

  • Counter for times of fitnessgbest with the same value

9: gbesttemp ←gbest  
10: fitnesstemp ←fitnessgbest  
11: for each iteration 
12: for each particle in P  
13:  v←UPDATE_v(p, v, pbest, gbest)

  • Update particle’s velocity

14:  p←UPDATE_p(p, v)

  • Update particle’s position

15:  fitnesscurrent ←COMPUTEFITNESS(p)

  • Compute current fitness

16:  fitnesspbest ←COMPUTEFITNESS(pbest)

  • Compute particle’s best fitness

17:  if fitnesscurrent<fitnesspbest then  
18:   pbest←p  
19:   fitnesspbest ←fitnesscurrent  
20:  if fitnesspbest<fitnesstemp then  
21:   gbesttemp ←pbest  
22:   fitnesstemp ←fitnesspbest  
23: if fitnesstemp<fitnessgbest then  
24:  gbest←gbesttemp  
25:  fitnessgbest ←fitnesstemp  
26:  count←0 
27: else  
28:  count←count+1 
29: if count >tf then

  • Trap into the local optimum

30:  for each particle in P

  • Apply restart strategy

31:   v←INITIALIZE_V()

  • Initial particle’s velocity

32:   p←INITIALIZE_P()

  • Initial particle’s position

33:   pbest←INITIALIZE_PB()

  • Initial particle’s pbest

34:  count←0