Function

Definition

Property

SCH1

min f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) s .t . x [ 5 , 7 ]

f 1 ( x ) = x 2

f 2 ( x ) = ( x 2 ) 2

Convex

SCH2

min f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) s .t . x [ 5 , 10 ]

f 1 ( x ) = { x , ( x 1 ) 2 + x , ( 1 < x 3 ) 4 x , ( 3 < x 4 ) 4 + x , ( x > 4 )

f 2 ( x ) = ( x 5 ) 2

Discontinuous

ZDT2

min f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) s .t . x [ 5 , 10 ]

f 1 ( x ) = x 1

f 2 ( x ) = g ( x ) [ 1 ( x 1 / g ( x ) ) 2 ]

g ( x ) = 1 + 9 ( i = 2 n x i ) / ( n 1 )

Concave

ZDT3

min f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) s .t . x i [ 0 , 1 ]

f 1 ( x ) = x 1

f 2 ( x ) = g ( x ) [ 1 x 1 / g ( x ) x 1 g ( x ) sin ( 10 π x 1 ) ]

g ( x ) = 1 + 9 ( i = 2 n x i ) / ( n 1 )

Discrete