GTU BE 8th Semester 2181912 Optimization(Department Elective II) Summer 2018 Question Paper

Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE – SEMESTER ?VIII (NEW) – EXAMINATION ? SUMMER 2018
Subject Code: 2181912 Date: 30/04/2018
Subject Name: Optimization(Department Elective II)
Time: 10:30 AM to 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Enlist Minimization Methods. 03
(b) Define: Constraint Surface, Objective Function. 04
(c) Compare Quasi- Newton method & Newton – Raphson. 07
Q.2 (a) List out Application of Optimization. 03
(b) Enlist Minimization Methods & Explain Fibonacci Method in detail. 04
(c) State Kuhn-Tucker condition for Multi Variable Optimization with Inequality
Constraint.
07

OR
(c) Find the dimensions of a cylindrical tin (with top and bottom) made up of sheet metal
to maximize its volume such that the total surface area is equal to A0 = 24 p.
07
Q.3 (a) Write the Taylor?s Series Expansion of a function f (x). 03
(b) Define: Design Vector, Design Constraints. 04
(c) Differentiate Simplex Method & Simple Algorithm. 07
OR
Q.3 (a) Explain Bisection Method. 03
(b) Describe Lagrange?s method of multipliers for solving optimization Problems. 04
(c) Write Short note on Golden Section method. 07
Q.4 (a) What is Parametric Constraint? 03
(b) Short note on Genetic Algorithms. 04
(c) Application of Linear Programming. 07
OR
Q.4 (a) How many basic solutions can an LP problem have? 03
(b) What do you mean by Neural Network? Discuss. 04
(c) Explain optimization of Fuzzy System in detail. 07
Q.5 (a) State the Linear Programming Problem in Standard form. 03
(b) Explain Random Search methods. 04
(c) Classify Unconstrained Optimization Techniques. & Explain Grid Search method. 07
OR
Q.5 (a) What is difference between Interpolation & Elimination methods? 03
(b) What are the roles of Exploratory and Pattern moves in the Hooke- Jeeves method? 04
(c) Discuss Powell?s Method for Non Linear Programming in detail.
07
*************