(SEM V) THEORY EXAMINATION 2022-23 OPTIMIZATION TECHNIQUE

Course: B.Tech (Semester V)

Subject: Optimization Technique

Subject Code: KEE-055

Duration: 3 Hours

Total Marks: 100

Instructions: Attempt all sections. Assume suitable data if necessary.

Section A – Short Answer Questions (2 × 10 = 20 Marks)

Answer all questions briefly:
 

What is a merit function?

What is a quadratic form?

Define the infeasibility form.

Explain methods of finding initial Basic Feasible Solutions.

What is an interval of uncertainty?

Why is the scaling of variables important?

Give the definition of a genetic algorithm.

Explain the types of simulation.

Why is economic load dispatch required for power systems?

Write the importance of maintenance scheduling of machines.

Section B – Descriptive Questions (10 × 3 = 30 Marks)

Attempt any three:

Find the maximum of f(X)=2x1+x2+10f(X) = 2x_1 + x_2 + 10f(X)=2x1​+x2​+10 subject to g(X)=x1+2x22=3g(X) = x_1 + 2x_2^2 = 3g(X)=x1​+2x22​=3 using the Lagrange Multiplier Method. Also, find the effect of changing the right-hand side of the constraint.

What is a simplex? Describe the Simplex Method for solving linear programming problems.

Explain the Dichotomous Search method. Find the minimum of f=x(x−1.5)f = x(x - 1.5)f=x(x−1.5) in the interval (0.0, 1.00) to within 10% of the exact value.

Explain in detail the basic steps of CPM/PERT and their advantages and disadvantages.

Briefly explain maintenance scheduling of motors in a manufacturing industry.

Section C – Long Answer / Analytical Questions (10 × 5 = 50 Marks)

Attempt one question from each:

Q3.
(a) State the various methods available for solving a multivariable optimization problem with equality constraints,
or
(b) State the Kuhn–Tucker conditions. What is a convex programming problem, and what is its significance?

Q4.
(a) Use the Simplex Method to solve the following LP problem:
Maximize Z=3x1+5x2+4x3Z = 3x_1 + 5x_2 + 4x_3Z=3x1​+5x2​+4x3​
Subject to:
(i) 2x1+3x2≤82x_1 + 3x_2 ≤ 82x1​+3x2​≤8
(ii) 2x2+5x3≤102x_2 + 5x_3 ≤ 102x2​+5x3​≤10
(iii) 3x1+2x2+4x3≤153x_1 + 2x_2 + 4x_3 ≤ 153x1​+2x2​+4x3​≤15
and x1,x2,x3≥0x_1, x_2, x_3 ≥ 0x1​,x2​,x3​≥0.

or
(b) Find the initial basic feasible solution for the following transportation problem using the North-West Corner Rule method:

Q5.
(a) What is the Interval Halving Method? Explain its procedure with a suitable example.
or
(b) State the necessary and sufficient conditions for the unconstrained minimum of a function. Define a Unimodal Function.

Q6.
(a) Find the critical path and calculate the slack time for the given network.
or
(b) Write short notes on:

Fitness function

Genetic algorithm (GA) operator

Comparison of GA with traditional methods

Q7.
(a) Two units of a plant have fuel costs given by:
F1=0.2P12+40P1+120 Rs/hF_1 = 0.2P_1^2 + 40P_1 + 120 \, \text{Rs/h}F1​=0.2P12​+40P1​+120Rs/h
F2=0.25P22+30P2+150 Rs/hF_2 = 0.25P_2^2 + 30P_2 + 150 \, \text{Rs/h}F2​=0.25P22​+30P2​+150Rs/h
Determine the economic operating schedule and corresponding cost of generation for a total demand of 180 MW.
or
(b) Explain speed control method using fuzzy logic controller.