53127-mt----design Optimization

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Code No: 53127/MT M.Tech. – I Semester Supplementary Examinations, September, 2008 DESIGN OPTIMIZATION (CAD/CAM) Time: 3hours

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

1.a) b)

Find the maximum and minimum value of y=3x5-5x3 Give cannonical form of non-Linear programming problem.

2.

Find the dimensions of a rectangular parallelelopipe with largest volume whose sides are parallel to the coordinate planes to be inscribed in the ellipsoid.

3.

Solve by Golden Section method. Find min. of f(x)=x2-2x in [1,2.6] within an interval of uncertainty equal to 0.13 L0 where L0 is the original interval of uncertainty.

4.

1 Minimize f ( x1 , x2 ) = ( x1 + 1)3 + x2 3 Subject to g1 ( x1 , x2 ) = − x1 + 1 ≤ 0 g 2 ( x1 , x2 ) = − x2 ≤ 0

using exterior penalty function method. 5.a) b)

State five engineering applications of optimization. Define a stochasting problem and give two practical examples.

Contd…2

Code No: 53127/MT

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6.

Find the link lengths of the four-bar linkage as shown in the figure for minimum structural error.

7.

Explain exterior penalty function method.

8.

Write short notes on: a) Genetic Algorithms b) Search methods.

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