Research Article
A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems
Table 6
The experimental results of (a) MSIA, (b) ACO, and (c) FA for CEC′13 benchmark functions in 50 dimensions [
54].
| | Problem | Best | Average | Standard deviation | Maximum | Algorithms |
| | –1.40000000e + 003 | 3.47354192e + 003 | 8.27740523e + 003 | 1.05496319e + 005 | a | | –1.40000000e + 003 | –1.35428971e + 003 | 4.70646934e + 002 | 6.25649642e + 003 | b | | –1.40000000e + 003 | –1.39910071e + 003 | 3.68737654e + 001 | 4.92018509e + 002 | c |
| | –1.41000000e + 003 | 1.84206047e + 003 | 6.15229975e + 003 | 1.00498786e + 005 | a | | 1.58838476e + 006 | 5.58502270e + 006 | 1.12878507e + 006 | 6.68406976e + 006 | b | | –1.29205225e + 003 | 1.41883572e + 004 | 3.38098501e + 005 | 1.58121852e + 007 | c |
| | –1.41000000e + 003 | 1.81535300e + 003 | 6.46557329e + 003 | 1.05226948e + 005 | a | | –1.19999370e + 003 | 4.84702158e + 008 | 4.52354730e + 009 | 4.13826791e + 010 | b | | –1.19990718e + 003 | 3.82746531e + 006 | 1.45131998e + 008 | 7.77082609e + 009 | c |
| | –1.41000000e + 003 | 1.72163802e + 003 | 6.14342458e + 003 | 1.09589953e + 005 | a | | 3.70514417e + 004 | 4.91623674e + 004 | 8.55923168e + 003 | 6.31998448e + 004 | b | | –1.10000000e + 003 | –1.05559019e + 003 | 6.69675768e + 002 | 1.87691603e + 004 | c |
| | –1.41000000e + 003 | 1.71817869e + 003 | 5.85107760e + 003 | 9.79306370e + 004 | a | | –1.00000000e + 003 | –9.85375133e + 002 | 1.03364586e + 002 | 3.21895510e + 001 | b | | –1.00000000e + 003 | –9.99689256e + 002 | 1.52449018e + 001 | 3.11424940e + 001 | c |
| | –1.41000000e + 003 | 1.99558869e + 003 | 6.34248688e + 003 | 1.01974633e + 005 | a | | –8.99378954e + 002 | –8.91979873e + 002 | 4.34885611e + 001 | –2.80863653e + 002 | b | | –8.90187577e + 002 | –8.90104659e + 002 | 3.02193637e + 000 | –7.29051446e + 002 | c |
| | –1.41000000e + 003 | 1.54987687e + 003 | 5.83338980e + 003 | 8.44106665e + 004 | a | | –8.00000000e + 002 | –7.88309504e + 002 | 4.62373905e + 001 | –5.73943541e + 002 | b | | –8.00000000e + 002 | –7.99909427e + 002 | 2.05901988e + 000 | –7.04307186e + 002 | c |
| | –1.41000000e + 003 | 1.83411229e + 003 | 6.23354197e + 003 | 9.99010936e + 004 | a | | –6.79738489e + 002 | –6.79704207e + 002 | 3.88206288e − 002 | –6.79388983e + 002 | b | | –6.79943515e + 002 | –6.79889283e + 002 | 2.01173471e − 002 | –6.79477819e + 002 | c |
| | –1.41000000e + 003 | 1.75086618e + 003 | 5.50835728e + 003 | 9.66542362e + 004 | a | | –5.94391734e + 002 | –5.93477219e + 002 | 1.86712018e − 001 | –5.88456073e + 002 | b | | –5.99898297e + 002 | –5.99881850e + 002 | 1.20806497e − 001 | –5.92019062e + 002 | c |
| | –1.41000000e + 003 | 1.81780473e + 003 | 6.26400664e + 003 | 1.11999458e + 005 | a | | –4.99574735e + 002 | –4.87583068e + 002 | 7.67688548e + 001 | 3.58471374e + 002 | b | | –4.99967994e + 002 | –4.99789635e + 002 | 6.69373644e + 000 | –8.19969150e + 001 | c |
| | –1.41000000e + 003 | 2.00976090e + 003 | 6.69847722e + 003 | 1.06053345e + 005 | a | | –3.79849409e + 002 | –3.69899276e + 002 | 1.22865847e + 001 | –2.22256810e + 002 | b | | –1.40000000e + 003 | –1.39875811e + 003 | 5.40784967e + 001 | 1.82944608e + 003 | c |
| | –1.41000000e + 003 | 1.64169743e + 003 | 6.32203970e + 003 | 1.14669794e + 005 | a | | –2.79898809e + 002 | –2.70056788e + 002 | 1.15344465e + 001 | –1.24564014e + 002 | b | | –1.28034976e + 003 | 1.27153310e + 004 | 1.10178983e + 005 | 3.51107348e + 006 | c |
| | –1.41000000e + 003 | 1.63715788e + 003 | 6.16915673e + 003 | 1.00990637e + 005 | a | | –1.79369746e + 002 | –1.69530534e + 002 | 1.36496165e + 001 | –4.88058640e + 001 | b | | –1.40000000e + 003 | –1.39910071e + 003 | 3.68737654e + 001 | 4.92018509e + 002 | c |
| | –1.41000000e + 003 | 1.73778253e + 003 | 5.98501382e + 003 | 1.07192661e + 005 | a | | 1.28527965e + 003 | 1.52502262e + 003 | 1.00139634e + 002 | 1.88113886e + 003 | b | | –1.29205225e + 003 | 1.41883572e + 004 | 3.38098501e + 005 | 1.58121852e + 007 | c |
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