Function
Define
Feature
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 type
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 − 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 type
ZDT3
min f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) , s . t . x i ∈ [ 0 , 1 ]
f 2 ( x ) = g ( x ) [ 1 − x 1 / g ( x ) − x 1 g ( x ) sin ( 10 π x 1 ) ]
Discrete type