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

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Code: 17D04201

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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

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Max. Marks: 60

Answer all the questions

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1. Solve by mixed integer programming

   Maximize Z = -3x1 - 2x2 + 10,

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   Subject to: X1 - 2X2+ X3 = 5/2,

   2X1 + X2 + X4 = 3/2,

   xj ≥ 0 (j = 1, 2, 3, 4), x2 and x3 integer.

   This problem is in canonical form, with x3 and x4 optimal basic variables for the associated linear program

   OR

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   Summarizes the general procedure of Branch-and-bound for integer-programming maximization with flow chart.

2. Find the optimum solution of the following constrained multivariable problem:

   Minimize Z = x₁² + (X2 + 1)² + (X3 − 1)²

   Subject to x1 + 5x2 – 3x3 = 6.

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   OR

   Describe the solving process of constrained multivariable optimization problems with inequality constraints.

3. Describe the six steps involved in Genetic algorithm.

   OR

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   Compute the mutation and crossover in a genetic algorithm with real numbers. Explain in detail.

4. One of management's goals in FirstRanker.com in a goal programming problem is expressed algebraically as,

   3X1 + 4x2 + 2x3 = 60, where 60 is the specific numeric goal and the left-hand side gives the level achieved toward meeting this goal.

   1. 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.

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   2. 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

   Describe how the NSGA-Nondominated Sorting Genetic Algorithm differs from basic simple GA with example.

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5. Discover the advance optimization techniques for the design of four-bar mechanism.

   OR

   Explain application of optimization in design and analysis of springs and gears.

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