JNTU
JNTU B.Tech IV OPTIMIZATION TECHNIQUES IN ENGINEERING Previous Question Paper (July - 2023 - R16)
Question paper consists of Part A, Part B. Part A is compulsory (25 marks). In Part B, Answer any one question from each unit (10 marks each).
Part A
List different elimination methods used in unconstrained optimization.
Answer
Elimination methods for unconstrained optimization, primarily used for functions of a single variable, include:
- Unrestricted Search Method
- Exhaustive Search Method
- Dichotomous Search Method
- Interval Halving Method
- Fibonacci Search Method
- Golden Section Search Method
Outline Fibonacci method.
Answer
The Fibonacci method is a derivative-free iterative search technique used to find the global optimum (minimum or maximum) of a unimodal function within a specified interval [a, b]. It is more efficient than the bisection method because it uses the properties of Fibonacci numbers to reduce the search space by a specific ratio at each step.
The procedure follows these steps:
- Define the initial interval [a, b], the desired final interval length L, and the number of iterations n based on the condition Fn ≥ (b - a) / L, where Fn is the n-th Fibonacci number.
- Calculate two interior points within the current interval using Fibonacci ratios: x1 = a + (Fn-2 / Fn)(b - a) and x2 = a + (Fn-1 / Fn)(b - a).
- Evaluate the function at these points. Based on the comparison of f(x1) and f(x2), discard the sub-interval that does not contain the optimum.
- Repeat the process by placing a new point in the remaining interval until the desired precision is achieved, ensuring that only one new function evaluation is required per iteration.
What is variable metric method? Describe in detail.
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Explain the gradient of function and its importance in brief.
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Label the advantages of simulation.
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Outline the formulation of linear programming.
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What is branch and bound method? Discuss.
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Define variance, correlation and co-variance.
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What is unconstrained G.P? Explain.
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List non-traditional Optimization Algorithms.
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Part B
Find the minimum of the function f = λ5 - 5λ3 - 20λ + 5 by the Fibonacci search method in the interval (0, 5).
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Find the minimum of the function f(x) = 0.65 - (0.75/(1+x2)) - 0.65x tan-1(1/x) using the quadratic interpolation method with an initial step size of 0.1.
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Minimize f(x1, x2) = x1 - x2 + 2x12 + 2x1x2 + x22 starting from the point x = [1, 0]T using Powell’s method.
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Solve the following problem by Fletcher-Reeves method. Min y = 10 - x1 + x1x2 + x22. Take a starting point as (1, 1).
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Max Z = 5x1 + 12x2 + 4x3 Subjected to x1 + 2x2 + x3 ≤ 5; 2x1 - x2 + 3x3 = 2. Solve the L.P.P and find the effect of changing the constraints by using sensitivity analysis.
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Explain different types of simulation models used and discuss their limitations.
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Analyze the applications of simulation in inventory.
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Solve the following problem using Gomory’s cutting plane method. Minimize f = -3x1 - 4x2 Subject to 3x1 - x2 + x3 = 12; 3x1 + 11x2 + x4 = 66; xi ≥ 0, all xi are integers.
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Evaluate chance constrained algorithm in detail with a suitable example.
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Minimize the function f = x1-1x2-2 + x1x2 + x1x23 using Geometric Programming, where x1, x2 > 0.
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Explain the similarities and differences between Genetic Algorithm and Traditional Methods.
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