Table 4: Performance comparison among multimodal optimization algorithms for the test functions . The standard unit of the column ET is seconds (numbers in parentheses are standard deviations). Bold faced letters represent best results.

FunctionAlgorithmNODOFEET

Deterministic crowding62.4 (14.3) 1,760,199 (254,341)14.62 (2.83)
Probabilistic crowding84.7 (5.48) 2,631,627 (443,522)34.39 (5.20)
Sequential fitness sharing76.3 (7.08) 2,726,394 (562,723)36.55 (7.13)
Clearing procedure93.6 (2.31) 2,107,962 (462,622)28.61 (6.47)
CBN87.9 (7.78) 2,835,119 (638,195)37.05 (8.23)
SCGA97.4 (4.80) 2,518,301 (643,129)30.27 (7.04)
AEGA99.4 (1.39) 978,435 (71,135)10.56 (4.81)
Clonal selection algorithm90.6 (9.95) 5,075,208 (194,376)58.02 (2.19)
AiNet93.8 (7.8) 3,342,864 (549,452)51.65 (6.91)
CAB100 (2) 680,211 (12,547)7.33 (1.84)

Deterministic crowding9.37 (1.91) 832,546 (75,413)4.58 (0.57)
Probabilistic crowding15.17 (2.43) 1,823,774 (265,387)12.92 (2.01)
Sequential fitness sharing15.29 (2.14) 1,767,562 (528,317)14.12 (3.51)
Clearing procedure18 (0) 1,875,729 (265,173)11.20 (2.69)
CBN14.84 (2.70) 2,049,225 (465,098)18.26 (4.41)
SCGA4.83 (0.38) 2,261,469 (315,727)13.71 (1.84)
AEGA18 (0) 656,639 (84,213)3.12 (1.12)
Clonal selection algorithm18 (0) 4,989,856 (618,759)33.85 (5.36)
AiNet18 (0) 3,012,435 (332,561)26.32 (2.54)
CAB18 (0) 431,412 (21,034)2.21 (0.51)

Deterministic crowding52.6 (8.86) 2,386,960 (221,982)19.10 (2.26)
Probabilistic crowding79.2 (4.94) 3,861,904 (457,862)43.53 (4.38)
Sequential fitness sharing63.0 (5.49) 3,619,057 (565,392)42.98 (6.35)
Clearing procedure79.4 (4.31) 3,746,325 (594,758)45.42 (7.64)
CBN71.3 (9.26) 4,155,209 (465,613)48.23 (5.42)
SCGA94.9 (8.18) 3,629,461 (373,382)47.84 (0.21)
AEGA98 (2) 1,723,342 (121,043)12,54 (1.31)
Clonal selection algorithm89.2 (5.44) 5,423,739 (231,004)47.84 (6.09)
AiNet92.7 (3.21) 4,329,783 (167,932)41.64 (2.65)
CAB100 (1) 953,832 (9,345)8.82 (1.51)

Deterministic crowding44.2 (7.93) 2,843,452 (353,529)23.14 (3.85)
Probabilistic crowding70.1 (8.36) 4,325,469 (574,368)49.51 (6.72)
Sequential fitness sharing58.2 (9.48) 4,416,150 (642,415)54.43 (12.6)
Clearing procedure67.5 (10.11) 4,172,462 (413,537)52.39 (7.21)
CBN53.1 (7.58) 4,711,925 (584,396)61.07 (8.14)
SCGA87.3 (9.61) 3,964,491 (432,117)53.87 (8.46)
AEGA90.6 (1.65) 2,213,754 (412,538)16.21 (3.19)
Clonal selection algorithm74.4 (7.32) 5,835,452 (498,033)74.26 (5.47)
AiNet83.2 (6.23) 4,123,342 (213,864)60.38 (5.21)
CAB97 (2) 1,121,523 (51,732)12.21 (2.66)