Improved Cuckoo Search (ICS) algorthm for constrained optimization

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f X gi X

0

hj X

0

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f X gj X

0 hj X

i

1,..., ng

j

ng ,..., nh

x1, x 2 ,..., xn

T

ng

0

nh

ng

F X

f X

P X, k j

P X, k j ng

P X, k j

j 1

k j max 0, g j X

2

kj

pa

0,1

n

t 1

xi

t

xi

Levy

t

0

Le vy

u

t

1

3

L / 100

L

pa pa

pa pa pa

pa

pa

rand * pa / gn

exp 1 / gn

gn pa

d D

x2

N

f x g1 x

x3 1

2 x 2x12 x 23x 3

71785x14

0

x3

x1

g2 x

4x 22

x1x 2

12566 x 2x13

g3 x

0.05

5108x12

x14

140.45x1

1

x1

1

1.5 2, 0.25 x 2

x1

1

0,

0,

x 22x 3

x2

g4 x

1

0,

1.3, 2.0

x3

15.0

x1 x2 x3

g1 x g2 x g3 x

g4 x

f x

PC

h t

x3

b

x4

f x

1.10471x12x 2

g2 x g3 x

0.04811x 3x 4 14

g1 x

x

x

max

x1

x4

max

0 0

0

x2

x1

l

x2

0.1047x12

g4 x

g5 x

0.04811x 3x 4 14

0.125 x1

g6 x g7 x

2

x

R

x 22

x1

4

x 22

2 2x1x 2

x

P

6000 lb L

12

x3

12 106 psi

0.125

x1

10

6PL

x

x 4x 32

2

PC x

2 14 in

PC x

max

max

0.1

x2

10

0

MR M J

Ex 32x 4

L

0.1

P L

4PL3

2

13600 psi

0

0

4.013E x 32x 46 / 36

0.25 in E

5.0

0

2x1x 2

2

x1

max

P

2R

x3

P

2

2

J

G

x2

2

x

x2

1

x3

E 2L 4G

30 106 psi max

x3

30000 psi

10 0.1

x4

5

x2 2

x1 x2 x3 x4

g1 x g2 x g3 x

g4 x g5 x g6 x

g7 x

f x

Ts Th

x2

R

L

x3

x4 x1

x2

f ( x)

0.625in

0.6224x1 x 3x 4

g1( x) g2 ( x) g3 ( x)

x2 x 32x 4

g4 ( x) X

x 1, x 2 , x 3 , x 4

T

1.7781x2x 32

x1

3.1661x12x 4

0.0193x 3

0.00954x 3

0

0

4 3 x 1296000 3 3 x 4 240 0

0

19.84x12x 3

x1

0 x4

10

x1

99

0

200

x1 x2 x3 x4

g1 x g2 x g3 x

g4 x

f x

g5 ( x)

1.1 x1

0,

g6 ( x)

0.6 x2

0

x2

99 10

x3

200

x1 x2 x3 x4

g1 x

g2 x g3 x g4 x

g5 x g6 x

f x

b

x1

m l1

x2

z

x4

l2 d2

x3

x5

d1

x7

0.7850x1x 22 3.3333x 32

f ( x) 1.508x1 x 62

x 72

7.477 x 63

g1 x g2 x g3 x g4 x

397.5 x1x 22x 32 1.93x 43 x 2x 3x 64 1.93x 53 x 2x 3x 74

x 73

14.9334x 3 0.7854 x 4x 63

27 x1x 22x 3 1

0

1

0

1

0

1

0

43.0934 x 5x 72

x6

2

745x 4 / x 2x 3 g5 x

16.9 106

110x 63 2

745x 5 / x 2x 3 g6 x

x 2x 3 40 5x 2

g8 x

x1

x1

g9 x g10 x

g11 x

12x 2 1.5x 6

1

0

1

0

1

0

1.9

x4

1.1x 7

1.9

x5

2.6

7.3

x4

8.3

7.3

x5

8.3

2.9

x6

3.9

0

1

0

157.5 106

85x 73

g7 x

1

1

0

1

0.

x1

5.0

3.6

x7

0.7

5.5

x2

0.8

17

x3

28

x1 x2 x3 x4 x5 x6 x7

g1 x g2 x

g3 x g4 x g5 x

g6 x g7 x g8 x

g9 x g10 x g11 x

f x