Download JNTUA M.Tech 1st Sem 2019 Feb Regular and Supply 17D04201 Advanced Optimization Techniques Question Paper

Download JNTUA (JNTU Anantapur) M.Tech ( Master of Technology) 1st Semester 2019 Feb Regular and Supply 17D04201 Advanced Optimization Techniques Previous Question Paper

Code: 17D04201

M.Tech I Semester Regular & Supplementary Examinations January/February 2019
ADVANCED OPTIMIZATION TECHNIQUES
(Common to PE&ED and PE)
(For students admitted in 2017 & 2018 only)

Time: 3 hours Max. Marks: 60

Answer all the questions

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1 Solve by mixed integer programming
Maximize Z = ?3x
1
? 2x
2
+ 10,
Subject to: x
1
? 2x
2
+ x
3
= 5/2 ,
2x
1
+ x
2
+ x
4
= 3/2,
x
j
? 0 (j = 1, 2, 3, 4), x
2
and x
3
integer.
This problem is in canonical form, with x
3
and x
4
optimal basic variables for the associated linear
program
OR
2 Summarizes the general procedure of Branch-and-bound for integer-programming maximization
with flow chart.

3 Find the optimum solution of the following constrained multivariable problem:
Minimize Z = x
1
2
+ (x
2
+ 1)
2
+ (x
3
? 1)
2

Subject to x
1
+ 5x
2
? 3x
3
= 6.
OR
4 Describe the solving process of constrained multivariable optimization problems with
inequality constraints.

5 Describe the six steps involved in Genetic algorithm.
OR
6 Compute the mutation and crossover in a genetic algorithm with real numbers. Explain in
detail.

7 One of management?s goals in a goal programming problem is expressed algebraically as,
3x
1
+ 4x
2
+ 2x
3
= 60, where 60 is the specific numeric goal and the left-hand side gives the level
achieved toward meeting this goal.
(i) Letting y+ be the amount by which the level achieved exceeds this goal (if any) and y- the
amount under the goal (if any), show how this goal would be expressed as an equality constraint
when reformulating the problem as a linear programming model.
(ii) If each unit over the goal is considered twice as serious as each unit under the goal, what is
the relationship between the coefficients of y+ and y- in the objective function being minimized in
this linear programming model?
OR
8 Describe how the NSGA-Nondominated Sorting Genetic Algorithm differs from basic simple GA
with example.

9 Discover the advance optimization techniques for the design of four-bar mechanism.
OR
10 Explain application of optimization in design and analysis of springs and gears.

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