Research Article

A Selective Biogeography-Based Optimizer Considering Resource Allocation for Large-Scale Global Optimization

Table 2

The results of the CC_BBO, CC_UEMO, CC_SBBO, and CC_SaNSDE algorithms on the CEC’2010 benchmark problems.

FunctionStatsCC_BBOCC_UEMOCC_SBBOCC_SaNSDECC_CMAES

f1Best1.99e + 10↑7.94e + 09↑3.40e + 068.42e − 021.31e + 05↓
Mean2.22e + 101.17e + 101.40e + 092.07e+002.84e + 05
Std1.60e + 091.01e + 101.13e + 096.76e+002.28e + 04

f2Best3.98e + 03↑5.40e + 02‖4.62e+024.12e + 03↑2.81e + 03↑
Mean4.02e + 037.96e + 021.07e+034.41e + 034.43e + 03
Std6.43e + 011.88e + 022.06e+021.68e + 021.77e + 02

f3Best1.52e + 01↑9.71e + 00‖2.42e+001.64e + 01↑8.66e + 00↑
Mean1.54e + 011.04e + 011.07e+011.66e + 011.06e + 00
Std1.31e − 018.01e − 011.21e+003.05e − 013.49e − 01

f4Best4.11e + 14↑3.99e + 13↑1.25e + 131.08e + 12↓8.45e+05
Mean5.68e + 144.89e + 135.15e + 132.74e + 121.01e+06
Std1.19e + 148.56e + 122.96e + 133.19e + 129.37e+04

f5Best4.93e + 08↑2.13e + 08↑5.26e + 071.16e + 08↑6.81e + 07‖
Mean5.12e + 082.84e + 081.88e + 081.28e + 089.52e + 07
Std1.15e + 074.99e + 077.20e + 071.92e + 072.23e + 07

f6Best1.63e + 07↑2.66e + 06↑1.59e + 011.73e + 01‖8.64e − 01↓
Mean1.65e + 077.62e + 069.19e + 011.83e + 019.17e − 01
Std1.62e + 053.41e + 062.94e + 005.70e + 014.23e − 01

f7Best9.27e + 10↑1.33e + 10‖8.92e + 092.07e + 01↓6.84e − 19↓
Mean1.02e + 112.07e + 102.44e + 102.16e + 017.41e − 19
Std8.00e + 091.01e + 108.72e + 097.57e + 008.35e − 20

f8Best1.72e + 15↑4.09e + 12↑2.06e + 083.14e + 05↓1.21e − 17↓
Mean2.34e + 151.61e + 155.95e + 145.59e + 057.97e+05
Std6.99e + 143.26e + 151.31e + 152.97e + 051.63e+06

f9Best5.90e + 09↑1.13e + 09↑2.04e + 084.28e + 07↓4.23e+06
Mean6.26e + 091.54e + 091.11e + 094.70e + 074.82e+06
Std2.20e + 083.31e + 081.58e + 095.22e + 065.25e+05

f10Best7.03e + 03↑3.12e + 03↑2.48e + 034.26e + 03↑2.64e + 03‖
Mean7.07e + 033.41e + 033.08e + 034.33e + 032.88e + 03
Std4.90e + 011.82e + 023.97e + 021.39e + 021.29e + 02

f11Best1.82e + 02↑6.58e + 01↑2.18e + 012.34e + 01‖1.49e − 12
Mean1.84e + 027.93e + 016.50e + 015.96e + 013.58e − 02
Std9.94e − 011.03e + 012.12e + 012.75e + 011.79e − 01

f12Best1.24e + 06↑2.49e + 05↑1.49e + 041.25e + 03↓3.12e − 22↓
Mean1.28e + 062.89e + 052.19e + 041.53e + 034.23e − 22
Std2.32e + 044.15e + 041.11e + 034.66e + 028.39e − 23

f13Best2.97e + 10↑1.29e + 10↑1.98e + 086.59e + 02↓3.21e+00↓
Mean3.19e + 101.55e + 108.50e + 097.41e + 025.90e+00
Std2.19e + 091.91e + 097.23e + 092.57e + 024.01e+00

f14Best1.13e + 10↑1.12e + 09↑3.62e + 083.88e + 08‖3.17e − 20↓
Mean1.17e + 101.43e + 098.11e + 083.97e + 083.91e − 20
Std2.73e + 082.79e + 085.62e + 082.31e+072.12e − 21

f15Best1.01e + 04↑4.45e + 03‖4.41e + 035.78e + 03‖1.91e + 03‖
Mean1.02e + 044.82e + 035.13e + 035.84e + 031.95e + 03
Std9.09e + 013.35e + 024.37e + 021.01e + 021.11e + 02

f16Best3.31e + 02↑1.26e + 02↑4.79e + 012.56e − 138.24e − 13↓
Mean3.33e + 021.46e + 029.00e + 012.67e − 138.44e − 13
Std1.33e + 001.80e + 011.49e + 019.81e − 152.10e − 14

f17Best2.04e + 06↑3.27e + 05↑3.13e + 044.01e + 04↑6.72e − 24
Mean2.14e + 063.57e + 054.27e + 044.08e + 046.91e − 24
Std8.06e + 041.99e + 043.64e + 032.56e + 032.06e − 25

f18Best5.85e + 10↑2.01e + 10‖3.51e + 081.01e + 03↓1.46e+01
Mean6.19e + 103.88e + 103.42e + 101.19e + 031.50e+01
Std1.95e + 091.70e + 101.48e + 101.69e + 027.20e+00

f19Best3.96e + 07↑6.26e + 06↑1.29e + 061.71e + 06‖5.31e+03↓
Mean4.51e + 079.14e + 061.77e + 061.73e + 065.47e+03
Std7.12e + 063.61e + 065.50e + 057.52e + 047.08e+02

f20Best3.74e + 12↑2.56e + 11↑2.23e + 113.87e + 03↓8.47e+02↓
Mean9.98e + 129.86e + 113.54e + 114.09e + 038.27e+02
Std4.46e + 114.94e + 111.25e + 113.29e + 036.35e+01

Note. The notation “↑/‖/↓” represents that CC_SBBO generated statistically “better/equally-well/worse” solution than the other algorithms. The best performances are highlighted bold.