53205-mt----optimization Techniques

NR

Code No: 53205/MT

M.Tech. – II Semester Regular Examinations, September, 2008 OPTIMIZATION TECHNIQUES (Machine Design) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

What is meant by mathematical models of a real solution? Discuss the importance of models in the solution of optimization problems. What are the various methods of optimization techniques? Discuss.

2.

Solve the following linear programming problems: Max. Z = x1 + x2 + 3 x3 − x4 Subjected to x1 + 2 x2 + 3 x3 = 15 2 x1 + x2 + 5 x3 = 20 x1 + 2 x2 + x3 + x4 = 10 x1 , x2 , x3 ≥ 0

3.

Solve the following assignment problem:

Job \ Machine A B C D E 4.

1 11 9 13 21 14

2 17 7 16 24 10

3 8 12 15 17 12

4 16 6 12 28 11

5 20 15 16 26 15

Find the extreme points of the function: f ( x1 , x2 ) = x13 + x23 + 2 x12 + 4 x22 + 6

Contd…2

Code No: 53205/MT 5.

Minimize

::2::

f ( x1 , x2 ) = x1 − x2 + 2 x12 + 2 x1 x2 + x22 starting from the point

0  X 1 =   , take ∆x1 = ∆x2 = 0.8 and C = 0.1. 0  6.

Minimize f = 4 x12 + 3 x22 − 5 x1 x2 − 8 x , starting from point (0, 0) using Powel’s method. Perform four iterations.

7.a)

What are the basic operations used in Genetic Algorithms? Explain. Construct the objective function to be used in Genetic Algorithms for a minimization problem with mixed equality and in equality constraints.

b)

8.a) b) c)

What is neural network? How is the error in the output minimized during network training? How is the fuzzy feasible domain defined for a problem with inequality constraints? Explain briefly the working principle of simulated annealing. *****