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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- (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--- Content provided by FirstRanker.com ---
a - 2b = 2
-3a + 2b = 3
Where a, b, = 0 - 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 - - Using the method of Lagrange multipliers:
Minimize f(x) = (x1² + x2² + x3²)
Subject to: g1(x) = x1 - x2
g2(x) = x1 + x2 + x3 - 1 - 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) - (a) Write the steps involved in writing a sample genetic algorithm.
(b) Explain the Roulette wheel analogy for the reproduction procedure in genetic algorithms. - Explain the concept of genetic programming (GP) and write the procedure for solving differential equations using GP.
- (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. - 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 s and t, respectively. The bending stress in the beam is calculated as:
s = 6M / (bd²)
And average shear stress in the beam is calculated as:
t = 3V / (2bd)--- Content provided by FirstRanker.com ---
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, s = 165 MPa, t = 50 MPa.
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