Research Article
A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems
Table 3
The experimental results of (a) MSIA, (b) ACO, and (c) FA by solving the CEC′13 benchmark functions in 10 dimensions [
54].
| Problem | Optimum | Best | Average | Standard deviation | Maximum | Algorithms |
| | | –1.05787441e + 003 | −4.27478554e + 002 | 5.32520087e + 002 | 4.51919784e + 003 | a | 1.29020039e + 003 | 1.43497411e + 003 | 1.52524081e + 002 | 2.42391695e + 003 | b | –6.97608460e + 001 | −5.56706985e + 001 | 9.83861302e + 001 | 1.59094345e + 003 | c |
| | | –1.41000000e + 003 | −1.38038036e + 003 | 1.51705325e + 002 | 3.82948621e + 003 | a | 1.37302013e + 003 | 1.81027837e + 003 | 1.99350254e + 001 | 1.82017859e + 003 | b | 2.60622099e + 003 | 7.38929816e + 004 | 8.28530915e + 005 | 1.68940889e + 007 | c |
| | | –1.07775351e + 003 | −7.87135563e + 002 | 5.41473038e + 002 | 4.68688680e + 003 | a | 2.01161840e + 002 | 2.01275691e + 002 | 3.26119574e − 001 | 2.03212837e + 002 | b | –1.19999683e + 003 | 1.34713183e + 007 | 2.61331526e + 008 | 6.96041088e + 009 | c |
| | | –1.00000000e + 001 | 2.97380129e + 006 | 5.27084138e + 006 | 7.70958077e + 007 | a | 3.38294199e + 002 | 3.48198354e + 002 | 2.52233087e + 001 | 4.52178904e + 002 | b | –1.10000000e + 003 | –8.53652774e + 002 | 1.41482529e + 003 | 1.45950316e + 004 | c |
| | | –7.71635593e + 002 | –5.58888645e + 002 | 2.76514199e + 002 | 4.56991524e + 003 | a | 4.38988097e + 002 | 4.56925962e + 002 | 3.70758564e + 001 | 7.12211302e + 002 | b | –1.00000000e + 003 | –9.98683610e + 002 | 2.96836196e + 001 | –1.60926967e + 002 | c |
| | | –1.41000000e + 003 | –1.38210398e + 003 | 9.76743330e + 001 | 5.09148005e + 002 | a | 5.02238254e + 002 | 5.93002146e + 002 | 4.51529039e + 002 | 3.20047624e + 003 | b | –8.99935443e + 002 | –8.99208513e + 002 | 5.49981592e + 000 | –7.64788173e + 002 | c |
| | | –7.34688317e + 002 | –6.55445684e + 002 | 4.26933534e + 002 | 4.19502288e + 003 | a | 6.03841405e + 002 | 6.04103425e + 002 | 1.21304155e − 001 | 6.04659232e + 002 | b | –8.00000000e + 002 | –7.99515370e + 002 | 5.41047502e + 000 | –6.89237686e + 002 | c |
| | | –1.41000000e + 003 | –1.37613278e + 003 | 1.47628379e + 002 | 2.70449872e + 003 | a | 1.10019387e + 003 | 1.11529246e + 003 | 6.39077139e + 001 | 1.94034991e + 003 | b | –6.79882628e + 002 | –6.79814730e + 002 | 2.70757318e − 002 | –6.79706209e + 002 | c |
| | | –7.79223446e + 002 | –5.87923497e + 002 | 5.29115496e + 002 | 6.36559812e + 003 | a | 2.71131924e + 003 | 2.80638128e + 003 | 7.47686019e + 001 | 3.35948750e + 003 | b | –5.99730286e + 002 | –5.99653895e + 002 | 4.48506744e − 001 | –5.90984947e + 002 | c |
| | | –1.41000000e + 003 | –1.38722065e + 003 | 1.35985509e + 002 | 3.96291901e + 003 | a | 2.81293009e + 003 | 3.03118853e + 003 | 5.83771758e + 001 | 3.20391460e + 003 | b | –4.99955742e + 002 | –4.99294862e + 002 | 1.08319919e + 001 | –2.62831236e + 002 | c |
| | | –1.00003268e + 003 | –6.28496611e + 002 | 5.20374802e + 002 | 8.18200464e + 003 | a | 1.22181090e + 003 | 1.22284625e + 003 | 1.61905418e + 000 | 1.23616915e + 003 | b | –4.00000000e + 002 | –3.99480200e + 002 | 4.13754005e + 000 | –3.08463035e + 002 | c |
| | | –1.41000000e + 003 | –1.37818962e + 003 | 1.46117712e + 002 | 2.51374993e + 003 | a | 1.32080243e + 003 | 1.32256986e + 003 | 1.04244644e + 000 | 1.33641433e + 003 | b | –2.97015123e + 002 | –2.96424650e + 002 | 4.86448955e + 000 | –1.94232316e + 002 | c |
| | | –7.55127444e + 002 | –5.31346642e + 002 | 5.59678487e + 002 | 6.24369518e + 003 | a | –1.40000000e + 003 | –1.21823184e + 003 | 6.99597007e + 002 | 2.29375556e + 003 | b | –1.97015123e + 002 | –1.96411417e + 002 | 4.60497004e + 000 | –7.09293980e + 001 | c |
| | | –1.41000000e + 003 | –1.37461266e + 003 | 1.46565437e + 002 | 2.11257128e + 003 | a | 7.79045518e + 006 | 1.92214598e + 007 | 1.24536123e + 007 | 5.64788737e + 007 | b | –8.46930600e + 001 | –6.97385530e + 001 | 1.11122780e + 002 | 1.69479719e + 003 | c |
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