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

M.Tech I Semester Supplementary Examinations August/September 2018

ADVANCED OPTIMIZATION TECHNIQUES

(Common to PE & PEED)

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(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:
   Maximize Z = 5a - 2b
   Subject to: 2a + b ≤ 9
   

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   a - 2b ≤ 2
   -3a + 2b ≤ 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	-

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3. Using the method of Lagrange multipliers:
   Minimize f(x) = (x₁² + x₂² + x₃²)
   Subject to: g₁(x) = x₁ - x₂
   g₂(x) = x₁ + x₂ + x₃ - 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:
   

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   f(x) = 12.096x₁ + 21.504x₂ – 1.732x₁² - x₂² at (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.
   

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   (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 σ and τ, respectively. The bending stress in the beam is calculated as:
   σ = 6M / (bd²)
   And average shear stress in the beam is calculated as:
   τ = 3V / (2bd)
   

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   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:
   M = 140kN m, V = 24 kN, σ = 165 MPα, τ = 50 MPa.

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