Continuous Benchmark Functions - Self-Adaptive Heuristics for Evolutionary Computation - page 142

g07

Minimize
f ( x )= x 1 + x 2 + x 1 x 2 − 10) 2 +4( x 4 − 5) 2 +( x 5 − 3) 2

14 x 1 − 16 x 2 +( x 3 −

1) 2 +5 x 7 +7( x 8 − 11) 2 +2( x 9 − 10) 2 +( x 10 − 7) 2 +45

(A.25)

+2( x 6 −

constraints

g 1 ( x )= − 105 + 4 x 1 +5 x 2 − 3 x 7 +9 x 8 ≤ 0

g 2 ( x )=10 x 1 − 8 x 2 − 17 x 7 +2 x 8 ≤ 0

g 3 ( x )= − 8 x 1 +2 x 2 +5 x 9 − 2 x 10 ≤ 0

2) 2 +4( x 2 − 3) 2 +2 x 3 −

g 4 ( x )=3( x 1 − 7 x 4 − 120 ≤ 0

(A.26)

g 5 ( x )=5 x 1 +8 x 2 +( x 3 − 6) 2

− 2 x 4 − 40 ≤ 0

g 6 ( x )= x 1 +2( x 2 − 2) 2 − 2 x 1 x 2 +14 x 5 − 6 x 6 ≤ 0

8) 2 +2( x 2 − 4) 2 +3 x 5 − g 7 ( x )=0 . 5( x 1 − x 6 − 30 ≤ 0

g 8 ( x )= − 3 x 1 +6 x 2 + 12( x 9 − 8) 2 − 7 x 10 ≤ 0

where 10 for j =(1 ,..., 10), optimum x ∗ =(2 . 171 , 2 . 363 , 8 . 773 ,

5 . 095 , 0 . 990 , 1 . 430 , 1 . 321 , 9 . 828 , 8 . 280 , 8 . 375) T with f ( x ∗ )=24 . 30620906818, fea-
sible starting point x (0) =(3 , 1 , 6 , 10 , 1 , 4 , 2 , 1 , 8 , 8) T with f ( x (0) ) = 867.

− 10 ≤ x j ≥

g08

sin 3 (2 πx 1 )sin(2 πx 2 )
x 1 ( x 1 + x 2 )

Minimize

f ( x )= −

(A.27)

constraints

g 1 ( x )= x 1 −

x 2 +1 ≤ 0

(A.28)

4) 2

g 2 ( x )=1 − x 1 +( x 2 − ≤ 0

≤ x 1 ≤ ≤ x 2 ≤

10, optimum x ∗ =(1 . 227 , 4 . 245) T

where 0 10 and 0 with

=(1 , 4) T f ( x ∗ )= − 0 . 0958250414180359, feasible starting point x (0) with

f ( x (0) ) =2.879077639283126E-63.

g09

Minimize

f ( x )=( x 1 − 10) 2 +5( x 2 − 12) 2 + x 3 +3( x 4 − 11) 2 +10 x 5 +7 x 6 + x 7 − 4 x 6 x 7 − 10 x 6 − 8 x 7
(A.29)

constraints

127 + 2 x 1 +3 x 2 + x 3 +4 x 4 +5 x 5 ≤ g 1 ( x )= − 0

282 + 7 x 1 +3 x 2 +10 x 3 + x 4 −

g 2 ( x )= − x 5 ≤ 0

(A.30)

196 + 23 x 1 + x 2 +6 x 6 −

g 3 ( x )= − 8 x 7 ≤ 0

g 4 ( x )=4 x 1 + x 2 − 3 x 1 x 2 +2 x 3 +5 x 6 −

11 x 7 ≤ 0