1680 工程科学学报.第42卷，第12期 表4（续） Table 4(Continued) Function Evaluation criterion SCA PSO DE ABC m-SCA COSCA SCADE Average optimal value 2.8604×101.0885×102 85.6179 39.9649 33.5690 28.4280 2.6926×101 Standard deviation 8.6617×10 76.0792 5.6043×103 33.9144 12.7300 2.8280×10- 1.4726×10 Average optimal value 12.6590 6.0666×103 5.3471×105 6.3063×104 1.6795 2.0598 7.5412e-005 Standard deviation 15.1820 3.9077×10-3 3.1452×10- 2.0140×10-3 4.6889x10-1 3.0051×10-1 9.4555×10-5 Average optimal value 1.0554×101 4.1429 4.5135×10-2 5.4601×10 1.3485×10-2 2.0053×10-3 8.4372×10-3 Standard deviation 8.2888×102 4.7166 1.3457×102 1.6048×10- 8.1723×10-3 1.4012×10-3 7.3689×10-3 Average optimal value -3.7782×103 -4.1603×103 -8.4186×103 -1.1434×103 -3.7936×103 -4.1950×103 -1.2005×10 Fs Standard deviation 2.6104×102 7.9194×102 4.3777×102 1.8317×10 3.0895×102 3.3863×10 2.5311×102 Average optimal value 38.9470 87.9805 1.0705×102 6.1381 3.5872 0 Standard deviation 39.3920 28.1184 9.4636 2.5352 7.8018 0 0 Average optimal value 11.1310 1.4188×10- 1.8656×103 1.6109×10- 4.9953×10 1.2993×10-152.1282×105 Standard deviation 9.2878 2.3163×10 4.9290×10 2.7105×10-1 7.2695×10-3 1.4211×10-51.7605×105 Average optimal value 8.7567×101 7.9155×103 4.1185×10-3 3.6220×102 3.9031×10-2 0 0 Fu Standard deviation 3.3704×10-1 9.0220×103 1.0744×102 3.2998×10-2 7.2525×10-2 S 0 Average optimal value 1.3000×103 1.0510×10-2 1.3328×10-3 3.4010×10-2 2.7777×10-1 1.8111×10-1 3.4531×10 F12 Standard deviation 4.4303×103 3.1074×102 1.1565×103 3.2998×10-2 1.7035×10-1 1.0280×10-1 1.6551×10 Average optimal value 3.6900×105 6.0034×10-3 6.1145×105 7.3970×10- 1.9535 2.6406 8.1272×103 FB Standard deviation 7.8302×10 9.4010×103 3.6027×105 2.1983×10 7.1911×10-1 1.3379×10-1 2.2908×102 Average optimal value 1.5288 2.6083 9.9800×10 9.9800×10 1.1775 3.4976 9.9800×10 Fu Standard deviation 8.7639×10-1 2.3500 5.3934×10-16 4.0294×10-165.1443×101 2.5112 4.9981×106 Average optimal value 1.0426×10-3 2.2388×10-31.3288×103 8.9459×10- 5.3421×10 5.6655×10- 7.5165×10 F15 Standard deviation 3.5566×10 4.8585×10-33.5391×10-32.5167×101.0454×104 1.4934×10+ 1.5392×10 Average optimal value -1.0316 -1.0316 -1.0316 -1.0316 -1.0316 -1.0316 -1.0316 F16 Standard deviation 6.0391×105 4.4409×10-6 4.4409×10-16 4.4600×10-16 4.5772×10 9.5922×10-7 4.4409x106 Average optimal value 4.0059×10-1 3.9789×10- 3.9789×10-1 3.9789×10- 3.9793×10-1 3.9827×10-1 0.3980 F1 Standard deviation 3.3623×103 0 0 9.6549×10-13 6.4763×105 4.2222×10 0 Average optimal value 3.0001 3 3 3.0006 3 3.0001 3 F18 Standard deviation 2.0536×10 3.4807×1015 2.2204×10-15 1.5874×10-3 2.7799x10-5 8.7317×x105 3.1780×107 Average optimal value -3.8545 -3.8604 -3.8628 -3.8628 -3.8623 -3.8615 -3.8628 F19 Standard deviation 2.7837×10-3 3.6118×10-32.2204×10-5 7.3021×10-7 3.3231×10-4 1.3023×10-3 7.6401×101日 Average optimal value -2.9131 -3.1561 -3.3037 -3.3220 -3.3100 -3.1561 -3.3119 F20 Standard deviation 2.4164×101 1.2335×1014.0486×102 1.3698×10-12.1606×10-2 3.7641×10-23.0470×102 Average optimal value -2.2308 -7.3872 -9.5674 -10.1416 -9.9300 -9.6428 -9.7526 F2t Standard deviation 1.9616 3.0638 1.7941 5.0343×102 1.7054×10-1 1.2629 8.9107×10 Average optimal value -3.3632 -8.9467 -10.1484 -10.3785 -10.2330 -10.2540 -10.4029 Standard deviation 1.7261 2.6947 1.3709 8.7082×10-2 1.0363×10- 1.0668×10-1 1.4504 Average optimal value -4.1765 -9.0497 -1.0325×101 -1.0526×101 -1.0315×10 -1.0369×101 -10.5364 F23 Standard deviation 2.0941 2.7622 1.0621 2.8287×10-2 1.7846×10-1 1.2772×10-1 3.4495×104 Decision result +=/- 0/0/23 2/2/19 5/2/16 5/0/18 2/0/21 3/2/18表 4 (续) Table 4 (Continued) Function Evaluation criterion SCA PSO DE ABC m-SCA COSCA SCADE F5 Average optimal value 2.8604×104 1.0885×102 85.6179 39.9649 33.5690 28.4280 2.6926×101 Standard deviation 8.6617×104 76.0792 5.6043×101 33.9144 12.7300 2.8280×10−1 1.4726×10−1 F6 Average optimal value 12.6590 6.0666×10−3 5.3471×10−5 6.3063×10−4 1.6795 2.0598 7.5412e-005 Standard deviation 15.1820 3.9077×10−3 3.1452×10−5 2.0140×10−3 4.6889×10−1 3.0051×10−1 9.4555×10−5 F7 Average optimal value 1.0554×10−1 4.1429 4.5135×10−2 5.4601×10−1 1.3485×10−2 2.0053×10−3 8.4372×10−3 Standard deviation 8.2888×10−2 4.7166 1.3457×10−2 1.6048×10−1 8.1723×10−3 1.4012×10−3 7.3689×10−3 F8 Average optimal value −3.7782×103 −4.1603×103 −8.4186×103 −1.1434×104 −3.7936×103 −4.1950×103 −1.2005×104 Standard deviation 2.6104×102 7.9194×102 4.3777×102 1.8317×102 3.0895×102 3.3863×102 2.5311×102 F9 Average optimal value 38.9470 87.9805 1.0705×102 6.1381 3.5872 0 0 Standard deviation 39.3920 28.1184 9.4636 2.5352 7.8018 0 0 F10 Average optimal value 11.1310 1.4188×10−1 1.8656×10−3 1.6109×10−1 4.9953×10−3 1.2993×10−15 2.1282×10−15 Standard deviation 9.2878 2.3163×10−1 4.9290×10−4 2.7105×10−1 7.2695×10−3 1.4211×10−15 1.7605×10−15 F11 Average optimal value 8.7567×10−1 7.9155×10−3 4.1185×10−3 3.6220×10−2 3.9031×10−2 0 0 Standard deviation 3.3704×10−1 9.0220×10−3 1.0744×10−2 3.2998×10−2 7.2525×10−2 0 0 F12 Average optimal value 1.3000×103 1.0510×10−2 1.3328×10−5 3.4010×10−2 2.7777×10−1 1.8111×10−1 3.4531×10−5 Standard deviation 4.4303×103 3.1074×10−2 1.1565×10−5 3.2998×10−2 1.7035×10−1 1.0280×10−1 1.6551×10−4 F13 Average optimal value 3.6900×105 6.0034×10−3 6.1145×10−5 7.3970×10−4 1.9535 2.6406 8.1272×10−3 Standard deviation 7.8302×105 9.4010×10−3 3.6027×10−5 2.1983×10−4 7.1911×10−1 1.3379×10−1 2.2908×10−2 F14 Average optimal value 1.5288 2.6083 9.9800×10−1 9.9800×10−1 1.1775 3.4976 9.9800×10−1 Standard deviation 8.7639×10−1 2.3500 5.3934×10−16 4.0294×10−16 5.1443×10−1 2.5112 4.9981×10−16 F15 Average optimal value 1.0426×10−3 2.2388×10−3 1.3288×10−3 8.9459×10−4 5.3421×10−4 5.6655×10−4 7.5165×10−4 Standard deviation 3.5566×10−4 4.8585×10−3 3.5391×10−3 2.5167×10−4 1.0454×10−4 1.4934×10−4 1.5392×10−4 F16 Average optimal value −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 Standard deviation 6.0391×10−5 4.4409×10−16 4.4409×10−16 4.4600×10−16 4.5772×10−6 9.5922×10−7 4.4409×10−16 F17 Average optimal value 4.0059×10−1 3.9789×10−1 3.9789×10−1 3.9789×10−1 3.9793×10−1 3.9827×10−1 0.3980 Standard deviation 3.3623×10−3 0 0 9.6549×10−13 6.4763×10−5 4.2222×10−4 0 F18 Average optimal value 3.0001 3 3 3.0006 3 3.0001 3 Standard deviation 2.0536×10−4 3.4807×10−15 2.2204×10−15 1.5874×10−3 2.7799×10−5 8.7317×10−5 3.1780×10−7 F19 Average optimal value −3.8545 −3.8604 −3.8628 −3.8628 −3.8623 −3.8615 −3.8628 Standard deviation 2.7837×10−3 3.6118×10−3 2.2204×10−15 7.3021×10−7 3.3231×10−4 1.3023×10−3 7.6401×10−13 F20 Average optimal value −2.9131 −3.1561 −3.3037 −3.3220 −3.3100 −3.1561 −3.3119 Standard deviation 2.4164×10−1 1.2335×10−1 4.0486×10−2 1.3698×10−11 2.1606×10−2 3.7641×10−2 3.0470×10−2 F21 Average optimal value −2.2308 −7.3872 −9.5674 −10.1416 −9.9300 −9.6428 −9.7526 Standard deviation 1.9616 3.0638 1.7941 5.0343×10−2 1.7054×10−1 1.2629 8.9107×10−1 F22 Average optimal value −3.3632 −8.9467 −10.1484 −10.3785 −10.2330 −10.2540 −10.4029 Standard deviation 1.7261 2.6947 1.3709 8.7082×10−2 1.0363×10−1 1.0668×10−1 1.4504 F23 Average optimal value −4.1765 −9.0497 −1.0325×101 −1.0526×101 −1.0315×101 −1.0369×101 −10.5364 Standard deviation 2.0941 2.7622 1.0621 2.8287×10−2 1.7846×10−1 1.2772×10−1 3.4495×10−14 Decision result + /=/ − 0/0/23 2/2/19 5/2/16 5/0/18 2/0/21 3/2/18 — · 1680 · 工程科学学报，第 42 卷，第 12 期