Research Article
A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems
Table 7
The experimental results gathered by (a) MSIA, (b) ACO, and (c) FA by solving the CEC′13 in 50 dimensions [
54].
| | Problem | Best | Average | Standard deviation | Maximum | Algorithms |
| | –1.41000000e + 003 | 1.66138664e + 003 | 5.80597454e + 003 | 1.04737568e + 005 | a | | 1.44383602e + 003 | 1.68507771e + 003 | 1.20240236e + 002 | 2.31595933e + 003 | b | | –1.19990718e + 003 | 3.82746531e + 006 | 1.45131998e + 008 | 7.77082609e + 009 | c |
| | –1.41000000e + 003 | 1.73757754e + 003 | 6.32949555e + 003 | 1.06562975e + 005 | a | | 2.00748304e + 002 | 2.00994974e + 002 | 1.32241987e − 001 | 2.01380946e + 002 | b | | –1.10000000e + 003 | –1.05559019e + 003 | 6.69675768e + 002 | 1.87691603e + 004 | c |
| | –1.41000000e + 003 | 1.65456868e + 003 | 5.58184222e + 003 | 9.12960968e + 004 | a | | 3.28546329e + 002 | 3.39782429e + 002 | 1.46231581e + 001 | 5.23035189e + 002 | b | | –1.00000000e + 003 | –9.99689256e + 002 | 1.52449018e + 001 | 3.11424940e + 001 | c |
| | –1.41000000e + 003 | 1.76042499e + 003 | 6.21341629e + 003 | 1.10332739e + 005 | a | | 4.23505035e + 002 | 4.38285056e + 002 | 1.90225565e + 001 | 6.95578654e + 002 | b | | –8.90187577e + 002 | –8.90104659e + 002 | 3.02193637e + 000 | –7.29051446e + 002 | c |
| | –1.41000000e + 003 | 1.85396888e + 003 | 6.17159111e + 003 | 1.03570243e + 005 | a | | 5.01667133e + 002 | 5.80533254e + 002 | 9.81067479e + 002 | 1.58505896e + 004 | b | | –8.00000000e + 002 | –7.99909427e + 002 | 2.05901988e + 000 | –7.04307186e + 002 | c |
| | –1.41000000e + 003 | 1.62539741e + 003 | 5.79958004e + 003 | 1.02487124e + 005 | a | | 6.03679642e + 002 | 6.03785422e + 002 | 9.66042719e − 002 | 6.04406379e + 002 | b | | –1.40000000e + 003 | –1.39910071e + 003 | 3.68737654e + 001 | 4.92018509e + 002 | c |
| | –1.41000000e + 003 | 1.64131527e + 003 | 6.14062123e + 003 | 1.05186050e + 005 | a | | 1.10019387e + 003 | 1.10324808e + 003 | 2.94743305e + 001 | 1.49762916e + 003 | b | | –1.29205225e + 003 | 1.41883572e + 004 | 3.38098501e + 005 | 1.58121852e + 007 | c |
| | –1.41000000e + 003 | 1.80847280e + 003 | 6.63718254e + 003 | 1.02559292e + 005 | a | | 2.37478548e + 003 | 2.54293073e + 003 | 9.12159912e + 001 | 3.00312732e + 003 | b | | –1.19990718e + 003 | 3.82746531e + 006 | 1.45131998e + 008 | 7.77082609e + 009 | c |
| | –1.41000000e + 003 | 1.69081569e + 003 | 5.78391372e + 003 | 9.43656508e + 004 | a | | 2.28938148e + 003 | 2.62333094e + 003 | 8.80245575e + 001 | 3.44774393e + 003 | b | | –1.10000000e + 003 | –1.05559019e + 003 | 6.69675768e + 002 | 1.87691603e + 004 | c |
| | –1.41000000e + 003 | 1.81639194e + 003 | 6.40390942e + 003 | 9.39010015e + 004 | a | | 1.22091464e + 003 | 1.22195198e + 003 | 1.01433920e + 000 | 1.23395762e + 003 | b | | –1.00000000e + 003 | –9.99689256e + 002 | 1.52449018e + 001 | 3.11424940e + 001 | c |
| | –1.41000000e + 003 | 1.86194201e + 003 | 6.54569682e + 003 | 9.52988225e + 004 | a | | 1.31791601e + 003 | 1.31863180e + 003 | 9.99567055e − 001 | 1.34051854e + 003 | b | | –8.90187577e + 002 | –8.90104659e + 002 | 3.02193637e + 000 | –7.29051446e + 002 | c |
| | –1.41000000e + 003 | 2.03024682e + 003 | 6.43914792e + 003 | 1.08131375e + 005 | a | | –1.40000000e + 003 | –1.35739006e + 003 | 4.27324154e + 002 | 4.72562605e + 003 | b | | –8.00000000e + 002 | –7.99909427e + 002 | 2.05901988e + 000 | –7.04307186e + 002 | c |
| | –1.41000000e + 003 | 1.77597903e + 003 | 6.06248056e + 003 | 8.06134908e + 004 | a | | –1.40000000e + 003 | –1.35296994e + 003 | 5.19958849e + 002 | 8.55895569e + 003 | b | | –6.79943515e + 002 | –6.79889283e + 002 | 2.01173471e − 002 | –6.79477819e + 002 | c |
| | –1.41000000e + 003 | 1.60912036e + 003 | 5.97109732e + 003 | 9.13205274e + 004 | a | | 2.19090607e + 006 | 1.14588392e + 007 | 1.17502885e + 007 | 4.93585298e + 007 | b | | –5.99898297e + 002 | –5.99881850e + 002 | 1.20806497e − 001 | –5.92019062e + 002 | c |
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