Table 5 Comparison of results of ARACO, RACO, ACO_R, and methods inspired on the behavior of ants

Rosenbrock (R₂) \( \overrightarrow{x} \):[−5,10]ⁿ, n = 2

1.0 (74.8)

1.05

10.96

90.98

131.55

153.47

Sphere \( \overrightarrow{x} \):[−5.12,5.12]ⁿ, n = 6

1.0 (16.4)

2.86

47.62

1333.41

619.08

3047.80

Griewangk \( \overrightarrow{x} \):[−5.12,5,12]ⁿ, n = 10

16.61

1.0 (30) [97%]

46.33 [61%]

1668

-

1668 [52%]

Goldstein and Price \( \overrightarrow{x} \):[−2,2]ⁿ, n = 2

1.0 (17)

2.88

22.58

316.23

-

1377.88 [56%]

Martin and Gaddy \( \overrightarrow{x} \):[−20,20]ⁿ, n = 2

1.0 (16)

1.0

21.56

107.81

-

733.12 [20%]

B₂ \( \overrightarrow{x} \):[−100,100]ⁿ, n = 2

1.0 (19.8)

4.07

27.37

-

-

602.31

Rosenbrock (R₅) \( \overrightarrow{x} \):[-5,10]ⁿ, n = 5

2.01

1.0 (184.3)

13.49 [97%]

-

-

215.90 [90%]

Shekel (S_4,5) \( \overrightarrow{x} \):[0,10]ⁿ, n = 4

6.06 [87%]

1.0 (47.9) [56%]

16.43 [57%]

-

-

821.5 [5%]