JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

Operations Research

Course Objectives

After doing this subject student should know

• The various optimization techniques for single variable optimization problem
• Direct search methods and Gradient methods for multi variable un constraint Optimization problems
• Formulate a Geometric Programming model and solve it by using Arithmetic Geometric in equality theorem
• Simulate the system
• Thorough of state of art optimization techniques like Genetic Algorithms, simulated Annealing

Course Outcomes

For a given system, as per customer requirement it is required to

• Formulate optimization problem.
• Solve the problem by using a appropriate optimization techniques.

UNIT - I

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, Pattern search methods – Powell’s, Hook - Jeeves, Rosen brock 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 M & Two phase methods. Sensitivity analysis: Changes in the objective coefficients, constants& coefficients of the constraints. Addition and deletion of variables, constraints. Simulation – Introduction – Types- steps – applications: inventory & queuing – Advantages and disadvantages

R16 B.TECH AERONAUTICAL ENGG.

UNIT - IV

Integer Programming- Introduction – formulation – Gomory cutting plane algorithm – Zero or one algorithm, branch and bound method Stochastic Programming: Basic concepts of probability theory, random variables- distributions-mean, variance, correlation, co variance, joint probability distribution. Stochastic linear programming: Chance constrained algorithm.

UNIT - V

Geometric Programming: Polynomials – Arithmetic - Geometric inequality – unconstrained G.P- constrained G.P (≤ type only) Non Traditional Optimization Algorithms: Genetics Algorithm-Working Principles, Similarities, and Differences between Genetic Algorithm & Traditional Methods. Simulated Annealing- Working Principle-Simple Problems. Introduction to Particle Swarm Optimization (PSO)(very brief)

TEXT BOOKS:

• 1. Optimization theory & Applications / S. S. Rao / New Age International.
• 2. Optimization for Engineering Design, Kalyanmoy Deb, PHI

REFERENCES:

• 1. Operations Research by S. D. Sharma Kedarnath & Ramnath Publisher
• 2. Operation Research by Hamdy A Taha Pearson Educations
• 3. Optimization in operations research by Ronald L. Rardin Pearson Publisher
• 4. Optimization Techniques by Benugundu & Chandraputla, Pearson Asia.
• 5. Optimization Techniques theory and practice by M. C. Joshi, K. M. Moudgalya Narosa Publications R16 B.TECH AERONAUTICAL ENGG. B.TECH. CIVIL ENGINEERING