Problem
Function
CEC01
min f ( x ) = ∑ i = 1 D ( ∑ j = 1 i x j ) 2 s .t . g ( x ) = ∑ i = 1 D [ x i 2 − 5000 cos ( 0.1 π x i ) − 4000 ] ≤ 0
CEC02
min f ( x ) = ∑ i = 1 D ( ∑ j = 1 i M x j ) 2 s .t . g ( x ) = ∑ i = 1 D [ ( M x i ) 2 − 5000 cos ( 0.1 π M x i ) − 4000 ] ≤ 0
CEC03
min f ( x ) = ∑ i = 1 D [ x i 2 − 10 cos ( 2 π x i ) + 10 ] s .t . g 1 ( x ) = − ∑ i = 1 D x i sin ( 2 x i ) ≤ 0 , g 2 ( x ) = ∑ i = 1 D x i sin ( 2 x i ) ≤ 0
CEC04
min f ( x ) = ∑ i = 1 D − 1 [ 100 ( x i 2 − x i + 1 ) 2 + ( x i 2 − 1 ) 2 ] s .t . g 1 ( x ) = ∑ i = 1 D [ ( M 1 x i ) 2 − 50 cos ( 2 π M 1 x i ) − 40 ] ≤ 0 g 2 ( x ) = ∑ i = 1 D [ ( M 2 x i ) 2 − 50 cos ( 2 π M 2 x i ) − 40 ] ≤ 0
CEC05
min f ( x ) = ∑ i = 1 D [ x i 2 − 10 cos ( 2 π x i ) + 10 ] s .t . h 1 ( x ) = − ∑ i = 1 D x i sin ( x i ) = 0 h 2 ( x ) = ∑ i = 1 D x i sin ( π x i ) = 0 h 3 ( x ) = − ∑ i = 1 D x i cos ( x i ) = 0 h 4 ( x ) = ∑ i = 1 D x i cos ( π x i ) = 0 h 5 ( x ) = ∑ i = 1 D ( x i sin ( 2 | x i | ) ) = 0 h 6 ( x ) = − ∑ i = 1 D ( x i sin ( 2 | x i | ) ) = 0
CEC06
min f ( x ) = max ( x i ) y l = x 2 l − 1 , w l = x 2 l where l = 1 , ⋯ , D / 2 s .t . h 1 ( x ) = ∑ i = 1 D / 2 ( ∑ j = 1 i y j ) 2 = 0 h 2 ( x ) = ∑ i = 1 D / 2 ( ∑ j = 1 i w j ) 2 = 0
CEC07
min f ( x ) = max ( x i ) y l = x 2 l − 1 , w l = x 2 l where l = 1 , ⋯ , D / 2 s .t . g ( x ) = ∏ i = 1 D / 2 w i ≤ 0 h ( x ) = ∑ i = 1 D / 2 ( y i 2 − y i + 1 ) 2 = 0
CEC08
min f ( x ) = max ( x i ) s .t . h 1 ( x ) = ∑ i = 1 D ( ∑ j = 1 i x j ) 2 = 0 h 2 ( x ) = ∑ i = 1 D − 1 ( x i − x i + 1 ) 2 = 0
CEC09
min f ( x ) = ∑ i = 1 D x i s .t . g ( x ) = ∏ i = 1 D x i ≤ 0 h ( x ) = ∑ i = 1 D − 1 ( x i 2 − x i + 1 ) 2 = 0
CEC10
min f ( x ) = ∑ i = 1 D − 1 ( 100 ( x i 2 − x i + 1 ) 2 + ( x i − 1 ) 2 ) s .t . g 1 ( x ) = ∑ i = 1 D ( x i 2 − 10 cos ( 2 π x i ) + 10 ) − 100 ≤ 0 g 2 ( x ) = ∑ i = 1 D x i − 2 D ≤ 0 g 3 ( x ) = 5 − ∑ i = 1 D x i ≤ 0
CEC11
min f ( x ) = max { | x i | , 1 ≤ i ≤ D } s .t . g ( x ) = ∑ i = 1 D x i 2 − 100 D ≤ 0 h ( x ) = cos f ( x ) + sin f ( x ) = 0
CEC12
min f ( x ) = ∑ i = 1 D | x i | s .t . g ( x ) = ∑ i = 1 D x i 2 − 100 D ≤ 0 h ( x ) = ( cos f ( x ) + sin f ( x ) ) 2 − exp ( cos f ( x ) + sin f ( x ) ) − 1 + exp ( 1 ) = 0
CEC13
min f ( x ) = ∑ i = 1 D ( z i 2 − 10 cos ( 2 π z i ) + 10 ) , z i 2 = { x i 2 , if | x i 2 | < 0.5 0.5 r o u n d ( 2 x i ) , otherwise s .t . g 1 ( x ) = 1 − ∑ i = 1 D | x i | ≤ 0 g 2 ( x ) = ∑ i = 1 D x i 2 − 100 D ≤ 0 h ( x ) = ∑ i = 1 D 100 ( x i 2 − x i + 1 ) 2 + ∏ i = 1 D sin 2 ( x i − 1 ) π = 0
CEC14
min f ( x ) = ∑ i = 1 D − 1 g ( x i , x i + 1 ) + g ( x D , x 1 ) , g ( x i , x i + 1 ) = 0.5 + sin 2 ( x i 2 + x i + 1 2 ) − 0.5 ( 1 + 0.001 x i 2 + x i + 1 2 ) 2 s .t . g 1 ( x ) = cos 2 ( ∑ i = 1 D x i ) − 0.25 cos ( ∑ i = 1 D x i ) − 0.125 ≤ 0 g 2 ( x ) = exp ( cos ( ∑ i = 1 D x i ) ) − exp ( 0.25 ) ≤ 0
CEC15
min f ( x ) = ∑ i = 1 D [ y i 2 − 10 cos ( 2 π y i ) + 10 ] , y = M x s .t . g 1 ( x ) = 4 − ∑ i = 1 D | y i | ≤ 0 g 2 ( x ) = ∑ i = 1 D y − 4 ≤ 0
CEC16
min f ( x ) = ∑ i = 1 D [ 100 ( y i 2 − x i + 1 ) 2 + ( y i − 1 ) 2 ] , y = M x s .t . g 1 ( x ) = ∑ i = 1 D ( y i 2 − 10 cos ( 2 π y i ) + 10 ) ≤ 0 g 2 ( x ) = ∑ i = 1 D y i − 2 D ≤ 0 g 2 ( x ) = 5 − ∑ i = 1 D y i ≤ 0