Mathematical Problems in Engineering

Research Article

Adaptive Cat Swarm Optimization Algorithm and Its Applications in Vehicle Routing Problems

Table 6

The statistical results of the algorithms.
FunctionPSOAPSOCSOACSO
AverageStandard deviationAverageStandard deviationAverageStandard deviationAverageStandard deviation
F14.66 × 1043.94 × 1031.46 × 1017.28 × 1002.43 × 10−333.80 × 10−331.62 × 10−482.76 × 10−48
F23.74 × 10336.42 × 10334.55 × 1011.60 × 1011.50 × 10−192.59 × 10−194.40 × 10−246.61 × 10−24
F37.92 × 1042.85 × 1045.29 × 1033.68 × 1026.36 × 10−271.10 × 10−2645.04 × 10−468.73 × 10−46
F46.91 × 1016.46 × 1003.74 × 1004.14 × 10−12.92 × 10−165.06 × 10−161.33 × 10−252.31 × 10−25
F51.83 × 10103.53 × 1097.23 × 1032.91 × 1032.88 × 1013.86 × 10−22.84 × 1011.70 × 10−5
F63.89 × 1041.03 × 1042.59 × 1011.52 × 1012.51 × 1001.14 × 10−13.65 × 1002.08 × 10−1
F72.16 × 1095.53 × 1081.09 × 1034.58 × 1028.37 × 10−66.77 × 10−61.58 × 10−61.71 × 10−6
F8−5.69 × 1024.06 × 101−1.17 × 1038.78 × 1011.22 × 10392.12 × 1039−6.88 × 1025.27 × 102
F94.91 × 1042.63 × 1033.19 × 1024.51 × 1010000
F102.12 × 1016.89 × 10−21.77 × 1014.12 × 1008.88 × 10−1608.88 × 10−160
F111.09 × 1011.31 × 1004.87 × 10−11.09 × 10−10000
F125.97 × 1092.74 × 1095.88 × 1003.74 × 1002.04 × 10−11.67 × 10−14.24 × 10−15.79 × 10−2
F131.13 × 10103.68 × 1092.33 × 1011.45 × 1011.30 × 1005.53 × 10−12.68 × 10−41.74 × 10−6
F141.26 × 1014.37 × 1001.33 × 1005.74 × 10−14.33 × 1002.33 × 1001.12 × 1001.38 × 10−1
F151.79 × 10−21.64 × 10−21.01 × 10−34.60 × 10−58.14 × 10−43.56 × 10−43.51 × 10−42.22 × 10−6
F161.53 × 1042.61 × 104−1.03 × 1000−1.03 × 1017.17 × 10−4−1.02 × 1009.85 × 10−3
F171.83 × 1002.34 × 1003.98 × 10−104.02 × 10−17.39 × 10−33.98 × 10−12.97 × 10−5
F181.27 × 1082.06 × 1083.005.44 × 10−163.00 × 1008.84 × 10−43.43 × 1005.22 × 10−1
F19−2.07 × 10−333.58 × 10−33−3.86 × 1003.14 × 10−16−3.72 × 1001.07 × 10−1−2.99 × 1005.14 × 10−1
F2000−6.59 × 10−15.79 × 10−1−1.85 × 1007.13 × 10−1−1.33 × 1001.54 × 10−1
F21−3.59 × 10−22.85 × 10−2−3.47 × 1001.41 × 100−2.14 × 1008.35 × 10−1−1.02 × 1016.80 × 10−9
F22−1.91 × 10−21.40 × 10−2−1.04 × 1011.78 × 10−15−3.66 × 1001.04 × 100−1.04 × 1013.90 × 10−7
F23−1.10 × 10−21.89 × 10−3−7.83 × 1004.69 × 100−3.00 × 1007.05 × 10−1−1.05 × 1011.38 × 10−7