Engineering Optimization: Theory and Practice, Fourth Edition

7.22 Test Problems 473

Objective(minimization of weight of speed reducer):

f (X)= 0. 7854 x 1 x 22 ( 3333. 3 x 32 + 41. 9334 x 3 − 34. 0934 )− 1. 508 x 1 (x 62 +x^27 )

+ 7. 477 (x^36 +x 73 ) + 0. 7854 (x 4 x 62 +x 5 x^27 )

Constraints:

g 1 (x) = 27 x 1 −^1 x 2 −^2 x− 31 ≤ 1

g 2 (x)= 397. 5 x− 11 x 2 −^2 x− 32 ≤ 1

g 3 (x) = 1. 93 x 2 −^1 x 3 −^1 x^34 x− 64 ≤ 1

g 4 (x) = 1. 93 x 2 −^1 x 3 −^1 x^35 x− 74 ≤ 1

g 5 (x)=

[(

745 x 4

x 2 x 3

) 2

+ 6 ( 1. 9 ) 106

] 0. (^5) /
0. 1 x^36 ≤ 1001
g 6 (x)=

[(

745 x 5

x 2 x 3

) 2

+ 57 ( 1. 5 ) 106

] 0. (^5) /
0. 1 x 73 ≤ 508
g 7 (x)=x 2 x 3 ≤ 04
g 8 (x) : 5 ≤
x 1
x 2
≤ 2 : 1 g 9 (x)
g 10 (x) : 2. 6 ≤x 1 ≤ 3. 6 :g 11 (x)
g 12 (x) : 0. 7 ≤x 2 ≤ 0. 8 :g 13 (x)
g 14 (x) : 17 ≤x 3 ≤ 8 : 2 g 15 (x)
g 16 (x) : 7. 3 ≤x 4 ≤ 8. 3 :g 17 (x)
g 18 (x) : 7. 3 ≤x 5 ≤ 8. 3 :g 19 (x)
g 20 (x) : 2. 9 ≤x 6 ≤ 3. 9 :g 21 (x)
g 22 (x) : 5. 0 ≤x 7 ≤ 5. 5 :g 23 (x)
g 24 (x)=( 1. 5 x 6 + 1. 9 )x 4 −^1 ≤ 1
g 25 (x)=( 1. 1 x 7 + 1. 9 )x 5 −^1 ≤ 1
Optimum solution:
X∗= { 3. 50 .7 17.0 7.3 7.3 3.35 5. 29 }T, f∗= 9852. 22
7.22.5 Heat Exchanger Design [7.42]
Objective function:Minimizef (X)=x 1 +x 2 +x 3