Research Article

A Cuckoo Search Algorithm for Multimodal Optimization

Table 2

Performance comparison among multimodal optimization algorithms for the test functions . For all the parameters, numbers in parentheses are the standard deviations.

FunctionAlgorithmEPNMPRPADA NFE

CDE24.16 (2.77)0.9682 (0.0318)2.4873 (2.4891)0.8291 (0.8296)28453 (2345)
SDE18.56 (2.51)0.4655 (0.0636)30.21 (43.132)2.1162 (0.6697)31328 (945)
CP8.80 (1.95)0.2222 (0.0509)60.52 (56.056)6.9411 (0.9500)30743 (1032)
AEGA15.67 (2.21)0.3934 (0.0534)40.56 (10.111)3.2132 (0.2313)32045 (684)
CSA14.54 (3.12)0.3323 (0.0431)48.34 (8.343)3.8232 (0.4521)25050 (0)
AiNet16.78 (2.63)0.4264 (0.0321)37.32 (10.432)2.9832 (0.5493)25050 (0)
MCS24.73 (0.49)0.9898 (0.0170)0.900 (1.4771)0.2584 (0.1275)25582 (74)

CDE2.1 (0.20)0.7833 (0.0211)23.235 (7.348)2.9354 (0.3521)30074 (1621)
SDE2.3 (0.31)0.8245 (0.0145)20.745 (8.012)2.6731 (0.8621)31497 (245)
CP2.4 (0.25)0.8753 (0.0301)18.563 (5.865)2.3031 (0.7732)29746 (1114)
AEGA2.1 (0.10)0.7879 (0.0174)22.349 (6.231)3.0021 (0.6431)30986 (1027)
CSA2 (0)0.7098 (0.0025)32.859 (8.659)3.1432 (0.5431)25050 (0)
AiNet2 (0)0.7165 (0.0076)31.655 (6.087)3.2265 (0.3467)25050 (0)
MCS4.74 (0.25)0.9154 (0.0163)2.3515 (2.511)0.0109 (0.0428)26043 (112)

CDE4.12 (0.78)0.7285 (0.0342)3.546 (1.034)3.0132 (0.5321)29597 (1034)
SDE4.64 (0.54)0.7893 (0.0532)3.054 (1.127)2.864 (0.3271)32743 (964)
CP4 (0)0.7092 (0.0298)3.881 (1.154)3.3412 (0.4829)28463 (1142)
AEGA3.43 (0.33)0.6734 (0.0745)4.212 (1.312)3.9121 (0.8732)29172 (1044)
CSA3.76 (0.51)0.6975 (0.0828)4.002 (1.197)3.5821 (0.7498)25050 (0)
AiNet4 (0)0.7085 (0.0385)3.797 (1.002)3.3002 (0.6496)25050 (0)
MCS6.82 (0.75)0.9274 (0.0137)0.423 (0.064)0.6842 (0.0598)25873 (88)

CDE10.36 (1.60)0.8572 (0.1344)1.859 (0.952)0.5237 (0.0321)34156 (2321)
SDE10.36 (2.04)0.8573 (0.1702)1.268 (0.581)0.6927 (0.0921)32132 (975)
CP9.16 (1.76)0.7577 (0.1462)2.536 (0.890)0.6550 (0.0440)30863 (1002)
AEGA8.34 (1.32)0.6954 (0.1021)4.432 (1.232)0.7021 (0.0231)31534 (852)
CSA8 (0)0.6532 (0.1378)4.892 (1.003)0.7832 (0.0432)25050 (0)
AiNet8 (0)0.6438 (0.2172)4.921 (1.102)0.7753 (0.0326)25050 (0)
MCS12 (0)0.9998 (0.0003)0.011 (0.008)0.0060 (0.0012)25789 (121)

CDE6.21 (1.54)0.6986 (0.1893)4.029 (1.401)5.1514 (1.0351)31456 (975)
SDE5.34 (2.03)0.5812 (0.1992)5.075 (1.071)6.0117 (1.1517)32481 (1002)
CP6.04 (0.61)0.6312 (0.1771)4.657 (1.321)5.3177 (1.7517)33123 (563)
AEGA4 (0)0.4112 (0.0343)6.341 (1.034)7.8751 (1.652)32634 (843)
CSA4 (0)0.3998 (0.0212)6.151 (1.121)7.7976 (1.0043)25050 (0)
AiNet4 (0)0.4034 (0.0973)6.003 (1.735)7.6613 (1.1219)25050 (0)
MCS9.65 (1.45)0.9411 (0.0087)0.015 (0.009)0.1043 (0.0864)25832 (65)

CDE13 (0)1 (0)0.010 (0.003)0.031 (0.0098)31572 (962)
SDE13 (0)1 (0)0.008 (0.004)0.021 (0.0065)33435 (1201)
CP13 (0)1 (0)0.015 (0.002)0.037 (0.0065)31834 (799)
AEGA10.66 (1.21)0.8323 (0.0343)0.088 (0.033)0.096 (0.0098)32845 (1182)
CSA8.94 (2.34)0.7998 (0.0564)0.110 (0.088)0.113 (0.0104)25050 (0)
AiNet10.32 (1.52)0.8297 (0.0206)0.098 (0.075)0.087 (0.0086)25050 (0)
MCS13 (0)0.9997 (0.0134)0.011 (0.007)0.023 (0.0016)25740 (101)

CDE3.04 (1.34)0.6675 (0.0754)0.809 (0.101)176.54 (21.23)32273 (1004)
SDE3.55 (0.56)0.7017 (0.0487)0.675 (0.079)115.43 (34.21)30372 (965)
CP2.87 (1.23)0.6123 (0.0861)1.081 (0.201)202.65 (42.81)31534 (1298)
AEGA3 (0)0.6686 (0.0542)0.894 (0.076)150.32 (57.31)29985 (1745)
CSA3 (0)0.6691 (0.0231)0.897 (0.045)161.57 (27.92)25050 (0)
AiNet3.50 (0.25)0.7001 (0.0765)0.668 (0.097)121.43 (43.12)25050 (0)
MCS7.13 (0.81)0.9859 (0.0094)0.023 (0.010)17.62 (4.13)25786 (92)