Continuous Benchmark Functions - Self-Adaptive Heuristics for Evolutionary Computation - page 143

10 for j =(1 ,..., 7), optimum x ∗ =(2 . 330 , 1 . 951 ,

with − 10 ≤ x j ≤ − 0 . 477 , 4 . 365 ,

0 . 624 , 1 . 038 , 1 . 594) T with f ( x ∗ ) = 680 . 630057374402, feasible starting point
x (0) =(0 , 0 , 0 , 0 , 0 , 0 , 0) T

−

with f ( x (0) ) = 1183 . 0.

g11

Minimize

x 1 +( x 2 − 1) 2

f ( x )= − (A.31)

constraints

x 1 = 0 h ( x )= x 2 − (A.32)

1, optimum x ∗ =(

where − 1 ≤ x 1 ≤ 1and − 1 ≤ x 2 ≤ − 0 . 707036070037170616 ,

0 . 00000004333606807) T with f ( x ∗ )=0 . 7499.

g12

Minimize

− 100 5) 2 / 100

5) 2 5) 2 f ( x )= − ( x 1 − − ( x 2 − − ( x 3 − (A.33)

constraints

p ) 2 +( x 2 − q ) 2 r ) 2 g ( x )=( x 1 − − ( x 3 − − 0 . 0625 ≤ 0 (A.34)

“where 0 10 ( i =1 , 2 , 3) and p, q, r =1 , 2 ,..., 9.Thefeasibleregionof

the search space consists of 9 3 disjoined spheres. A point ( x 1 ,x 2 ,x 3 ) T is feasible,
iff there exist p, q, r such that the above inequality holds. The optimum is located
at x =(5 , 5 , 5) T

≤ x i ≤

where f ( x )= − 1. The solution lies within the feasible region.”

[83]

g16

Minimize
f ( x )=0 . 000117 y 14 +0 . 1365 + 0 . 00002358 y 13 +0 . 000001502 y 16 +0 . 0321 y 12
+0 . 004324 y 5 +0 . 0001 c 15

c 16 +37 . 48 y 2

c 12 −

0 . 0000005843 y 17

(A.35)

constraints

g 1 ( x )= 0 . 28

0 . 72 y 5 −

y 4 ≤ 0

g 2 ( x )= x 3 − 1 . 5 x 2 ≤ 0

.
g 37 ( x ) = 2802713

(A.36)

− y 17 ≤ 0

g 38 ( x )= y 17 − 12146108 ≤ 0