Table 3: Performance comparison among the multimodal optimization algorithms for the test functions . The standard unit in the column ET is seconds. (For all the parameters, numbers in parentheses are the standard deviations.) Bold faced letters represent best obtained results.

FunctionAlgorithmNODOFEET

Deterministic crowding5 (0) 7,153 (358)0.091 (0.013)
Probabilistic crowding5 (0) 10,304 (487)0.163 (0.011)
Sequential fitness sharing5 (0) 9,927 (691)0.166 (0.028)
Clearing procedure5 (0) 5,860 (623)0.128 (0.021)
CBN5 (0) 10,781 (527)0.237 (0.019)
SCGA5 (0) 6,792 (352)0.131 (0.009)
AEGA5 (0) 2,591 (278)0.039 (0.007)
Clonal selection algorithm5 (0) 15,803 (381)0.359 (0.015)
AiNet5 (0) 12,369 (429)0.421 (0.021)
CAB5 (0) 1,776 (125)0.020 (0.009)

Deterministic crowding3.53 (0.73) 6,026 (832)0.271 (0.06)
Probabilistic crowding4.73 (0.64) 10,940 (9517)0.392 (0.07)
Sequential fitness sharing4.77 (0.57) 12,796 (1,430)0.473 (0.11)
Clearing procedure4.73 (0.58) 8,465 (773)0.326 (0.05)
CBN4.70 (0.53) 14,120 (2,187)0.581 (0.14)
SCGA4.83 (0.38) 10,548 (1,382)0.374 (0.09)
AEGA5 (0) 3,605 (426)0.102 (0.04)
Clonal selection algorithm5 (0) 21,922 (746)0.728 (0.06)
AiNet5 (0) 18,251 (829)0.664 (0.08)
CAB5 (0) 2,065 (92)0.08 (0.007)

Deterministic crowding4.23 (1.17) 11,009 (1,137)1.07 (0.13)
Probabilistic crowding4.97 (0.64) 16,391 (1,204)1.72 (0.12)
Sequential fitness sharing4.87 (0.57) 14,424 (2,045)1.84 (0.26)
Clearing procedure6 (0) 12,684 (1,729)1.59 (0.19)
CBN4.73 (1.14) 18,755 (2,404)2.03 (0.31)
SCGA6 (0) 13,814 (1,382)1.75 (0.21)
AEGA6 (0) 6,218 (935)0.53 (0.07)
Clonal selection algorithm5.50 (0.51) 25,953 (2,918)2.55 (0.33)
AiNet4.8 (0.33) 20,335 (1,022)2.15 (0.10)
CAB6 (0) 4,359 (75)0.11 (0.023)


Deterministic crowding76.3 (11.4) 1,861,707 (329,254)21.63 (2.01)
Probabilistic crowding92.8 (3.46) 2,638,581 (597,658)31.24 (5.32)
Sequential fitness sharing89.9 (5.19) 2,498,257 (374,804)28.47 (3.51)
Clearing procedure89.5 (5.61) 2,257,964 (742,569)25.31 (6.24)
CBN90.8 (6.50) 2,978,385 (872,050)35.27 (8.41)
SCGA91.4 (3.04) 2,845,789 (432,117)32.15 (4.85)
AEGA95.8 (1.64) 1,202,318 (784,114)12.17 (2.29)
Clonal selection algorithm92.1 (4.63) 3,752,136 (191,849)45.95 (1.56)
AiNet93.2 (7.12) 2,745,967 (328,176)38.18 (3.77)
CAB100 (2) 697,578 (57,089)5.78 (1.26)