Download JNTUA M.Tech 1st Sem 2018 Aug-Sept 9D04201 Advanced Optimization Techniques Question Paper

Download JNTUA (JNTU Anantapur) M.Tech ( Master of Technology) 1st Semester 2018 Aug-Sept 9D04201 Advanced Optimization Techniques Previous Question Paper

Code: 9D04201


M.Tech I Semester Supplementary Examinations August/September 2018
ADVANCED OPTIMIZATION TECHNIQUES
(Common to PE & PEED)
(For students admitted in 2013, 2014, 2015 & 2016 only)

Time: 3 hours Max. Marks: 60

Answer any FIVE questions
All questions carry equal marks
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1 (a) Write the procedure involved in converting inequality constraints (both ?and ?) into equality constrains in
linear programming problems.
(b) Write the dual of the problem:
? ? ? = 5 ? ? 2 ?
Subject to: 2 ? + ? ? 9
? ? 2 ? ? 2
?3 ? + 2 ? ? 3
Where a, b, ? 0

2 A salesman wants to visit A, B, C, D and E. He does not want to visit any city twice before completing his
work. Find the least cost route.
A B C D E
A - 2 5 7 1
B 6 - 3 8 2
C 8 7 - 4 7
D 12 4 6 - 5
E 1 3 2 8 -


3 Using the method of Lagrange multipliers:
? ? ? ? ? ? ( ? ) =
1
2
( ? 1
2
+ ? 2
2
+ ? 3
2
)
Subject to: ? 1
( ? ) = ? 1
? ? 2

? 2
( ? ) = ? 1
+ ? 2
+ ? 3
? 1

4 Calculate the gradient of the following function at the given point by the central difference approach with
a 1 percent change in the point and compare them with the exact gradient:
? ( ? ) = 12.096 ? 1
2
+ 21.504 ? 2
2
? 1.732 ? 1
? ? 2
? (5,6)

5 (a) Write the steps involved in writing a sample genetic algorithm.
(b) Explain the Roulette wheel analogy for the reproduction procedure in genetic algorithms.

6 Explain the concept of genetic programming (GP) and write the procedure for solving differential
equations using GP.

7 (a) Explain the terms population, generation and niche used in genetic algorithms.
(b) Explain the applications of multi objective GA problems.

8 A beam of rectangular cross section is subjected to a maximum bending moment of M and a maximum
shear of V. The allowable bending and shearing stresses are ? and ?, respectively. The bending stress in
the beam is calculated as:
? =
6 ? ? ? 2

And average shear stress in the beam is calculated as:
? =
3 ? 2 ?

Where d is the depth and b is the width of the beam. It is also desired that the depth of the beam shall not
exceed twice its width. Formulate the design problem for minimum cross-sectional area using the
following data:
? = 140 ? ? ? , ? = 24 ? , ? = 165 ? , ? = 50 ? .
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