A Hybrid Global Optimization Algorithm: Particle Swarm Optimization in Association with a Genetic Algorithm - Complex System Modelling and Control Through Intelligent Soft Computations - page 59

Table 5 The comparison results among single-objective optimization algorithms for the Schwefel
2.22 function

GA (traditional
crossover)

GA (multiple-
crossover)

PSO
(standard)

The hybrid
algorithm

1.83 × 10 − 6 8.16 × 10 0 3.15 × 10 − 26 9.11 × 10 − 25

Mean

10 − 6 10 +1 10 − 25 10 − 24 Standard

deviation

4.32 × 3.13 × 1.73 × 4.99 ×

Table 6 The comparison results among single-objective optimization algorithms for the Schwefel
1.2 function

GA (traditional
crossover)

GA (multiple-
crossover)

PSO
(standard)

The hybrid
algorithm

7.74 × 10 +2 3.14 × 10 +2 6.73 × 10 − 5 2.14 × 10 − 11 Mean

10 +2 10 +2 10 − 5 10 − 11

Standard
deviation

4.16 × 1.99 × 9.40 × 6.91 ×

Table 7 The comparison results among single-objective optimization algorithms for the

Rosenbrock function
GA (traditional
crossover)

GA (multiple-
crossover)

PSO
(standard)

The hybrid
algorithm

10 +2 10 +1 10 +1 10 − 1

Mean 1.33 × 8.25 × 2.04 × 5.34 ×

10 +2 10 +1 10 +1 10 0

Standard
deviation

1.32 × 5.51 × 2.53 × 1.38 ×

Table 8 The comparison results among single-objective optimization algorithms for the Noise
function

GA (traditional
crossover)

GA (multiple-
crossover)

PSO
(standard)

The hybrid
algorithm

5.10 × 10 − 2 8.64 × 10 − 2 1.06 × 10 0 3.38 × 10 − 3 Mean

10 − 2 10 − 2 10 − 1 10 − 3 Standard

deviation

1.88 × 2.48 × 3.12 × 1.47 ×

Table 9 The comparison results among single-objective optimization algorithms for the Step
function

GA (traditional
crossover)

GA (multiple-
crossover)

PSO
(standard)

The hybrid
algorithm

2.10 × 10 +2 3.40 × 10 +1 1.00 × 10 − 1 Mean 0

10 +2 10 +2 10 − 1 Standard

deviation

3.27 × 1.32 × 3.05 × 0