R22 M.Tech. ENGG. DESIGN

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

###### M. TECH. I Year I Sem. (ENGG. DESIGN)

###### OPTIMIZATION TECHNIQUES & APPLICATIONS (Professional Elective - II)

L	T	P	C
3	0	0	3

Pre-requisites : Operations Research

Course Objectives: Objectives: The main objectives of the course are: Learn

- • optimization techniques for single variable and multi variable non- linear • optimization techniques for single variable and multi variable non- linear optimization problems.
- • analysis on LPP queuing • analysis on LPP queuing
- • of annexing problem & inventory problem. • of annexing problem & inventory problem.
- • cutting plane method & branch bound method for linear IPP. • cutting plane method & branch bound method for linear IPP.
- • of stochastic programming problem simple problems for finding mean variance of • of stochastic programming problem simple problems for finding mean variance of random variables chance constrained algorithm.
- • of GP model and solving it using arithmetic geometric inequality theorem. • of GP model and solving it using arithmetic geometric inequality theorem.
- • of art nontraditional optimization technique, namely genetic algorithm simulated • of art nontraditional optimization technique, namely genetic algorithm simulated annealing & particle swarm optimization.

Course Outcomes: Outcomes: At the end of the course, the student is able to apply appropriate optimization techniques and solve.

- • on the type of optimization problem like single variable or multivariable, • on the type of optimization problem like single variable or multivariable,
- • sensitivity analysis to study effect of changes in parameters of LPP on the optimal • sensitivity analysis to study effect of changes in parameters of LPP on the optimal solution without reworking.
- • the system to estimate specified performance measures. • the system to estimate specified performance measures.
- • integer programming problem by either geometry cutting plane algorithm or branch • integer programming problem by either geometry cutting plane algorithm or branch band method.
- • chance constrained algorithm and solve stochastic linear programme. • chance constrained algorithm and solve stochastic linear programme.
- • GP model and solve it. • GP model and solve it.
- • given optimization problem by genetic algorithm or simulated annealing or PSO. • given optimization problem by genetic algorithm or simulated annealing or PSO.

UNIT-I: Single Variable Non-Linear Unconstrained Optimization: Elimination methods: Uni-Model Single Variable Non-Linear Unconstrained Optimization: Elimination methods: Uni-Model function-its importance, Fibonacci method & Golden section method. Interpolation methods: Quadratic & Cubic interpolation methods.

UNIT-II: Multi variable non-linear unconstrained optimization: Direct search methods - Univariant method, Multi variable non-linear unconstrained optimization: Direct search methods - Univariant method, Pattern search methods - Powell's, Hook -Jeeves, Rosenbrock search methods. Gradient methods: Gradient of function& its importance, Steepest descent method, Conjugate direction methods: Fletcher-Reeves method & variable metric method.

UNIT-III: Linear Programming: Formulation, Simplex method & Artificial variable optimization techniques: Big Linear Programming: Formulation, Simplex method & Artificial variable optimization techniques: Big M & Two-phase methods. Sensitivity analysis: Changes in the objective coefficients, constants& coefficients of the constraints. Addition of variables, constraints. Simulation - Introduction - Types- steps - applications: inventory & queuing - Advantages and disadvantages

UNIT-IV: Integer Programming: Introduction - formulation - Geometry cutting plane algorithm - Zero or one Integer Programming: Introduction - formulation - Geometry cutting plane algorithm - Zero or one algorithm, branch and bound method