Table 4: Performance results of HPSO-SA, SUPER-SAPSO, SAPSO, and PSO algorithms on benchmark functions.

Function Algorithm Number of iterations Average Error

Rastrigin PSO 2989 0.097814
SAPSO 2168 0.07877
SUPER-SAPSO 5 0.0
HPSO-SA 2022.43 0.0

Sphere PSO 805 0.094367
SAPSO 503 0.085026
SUPER-SAPSO 4 0.0
HPSO-SA 501.15 7 , 9 2 𝑒 3 2

Griewank PSO 2004 0.082172
SAPSO 1517 0.075321
SUPER-SAPSO 3 0.0
HPSO-SA 1496.35 3 , 6 1 𝑒 2 0

Ackley PSO 4909 0.099742
SAPSO 3041 0.099461
SUPER-SAPSO 5 0.0
HPSO-SA 3020.65 8 , 9 2 𝑒 1 6