Continuous Benchmark Functions - Self-Adaptive Heuristics for Evolutionary Computation - page 141

g02

Minimize

i =1 cos 4 ( x i )

2 i =1 cos 2 ( x i ) −

f ( x )= − i =1 ix i (A.19)

constraints:

− i =1 x i ≤ g 1 ( x )=0 . 75 0

g 2 ( x )= i =1 x i −

(A.20)

7 . 5 N ≤ 0

with N=20, feasible intervals 0 <x j 10 for j =1 ,...,N ,bestknown

value x ∗ = (3.162, 3.128, 3.094, 3.061, 3.027, 2.993, 2.958, 2.921, 0.494, 0.488,
0.482, 0.476, 0.471, 0.466, 0.461, 0.456, 0.452, 0.448, 0.444, 0.440) T , f ( x ∗ )=
0 . 80361910412559, feasible starting point x (0)

≤

=(1 ,..., 1) T with f ( x (0) )=

0 . 117616.

g04 - Himmelblau's Problem

Minimize

f ( x )=5 . 3578547 x 3 +0 . 8356891 x 1 x 5 +37 . 293239 x 1 −

40792 . 141 (A.21)

constraints

g 1 ( x )=85 . 334407 + 0 . 0056858 x 2 x 5 +0 . 0006262 x 1 x 4 −

0 . 0022053 x 3 x 5
g 2 ( x )=80 . 51249 + 0 . 0071317 x 2 x 5 +0 . 0029955 x 1 x 2 +0 . 0021813 x 3
g 3 ( x )=9 . 300961 + 0 . 0047026 x 3 x 5 +0 . 0012547 x 1 x 3 +0 . 0019085 x 3 x 4
0

(A.22)

≤ g 1 ( x ) ≤ 92

90 ≤ g 2 ( x ) ≤ 110

20 ≤ g 3 ( x ) ≤ 25

45 ( i =3 , 4 , 5), minimum x ∗ =
(78 . 000 , 33 . 000 , 29 . 995 , 45 . 000 , 36 . 776) T with f ( x ∗ )=

with 78 ≤ x 1 ≤ 102, 33 ≤ x 2 ≤ 45 and 27 ≤ x i ≤

−

30665 . 53867178332.

g06

Minimize

10) 3 +( x 2 − 20) 3 f ( x )=( x 1 − (A.23)

constraints

g 1 ( x )= − ( x 1 − 5) 2 − ( x 2 − 5) 2 + 100 ≤ 0

(A.24)

6) 2 +( x 2 − 5) 2

g 2 ( x )=( x 1 − − 82 . 81 ≤ 0

where 13 ≤ x 1 ≤ 100 and 0 ≤ x 2 ≤ 100, minimum x ∗ =(14 . 09500000000000064 ,

0 . 8429607892154795668) T

6961 . 81387558015, both constraints
are active, feasible starting point x (0) =(6 , 9) T

with f ( x ∗ )= −

with f ( x (0) )= − 3250.