18ME754 Optimization Techniques syllabus for ME

Introduction:

Statement of optimisation problem, Design vector, Design constraints, Objective function, Classification of optimisation problems based on :constraints, nature of design variables, nature of the equations involved

Single variable optimisation:

Necessary and sufficient conditions, Multivariable optimization with no constraints: Necessary and sufficient conditions, Semi definite case, Saddle point, Multi variable optimization with equality constraints, Solution by direct substitution, Lagrange Multipliers, Interpretation of Lagrange multipliers, Multivariable optimization with inequality constraints: Khun Tucker conditions(concept only).

Nonlinear Programming:

One-Dimensional Minimization Methods, Introduction, Unimodal Function, Elimination methods: unrestricted search, fixed step size, accelerated step size, Exhaustive search: dichotomous search, interval halving method, Fibonacci method, golden section method, Interpolation methods: Quadratic and cubic interpolation method, direct root method, Newton method, QuasiNewton method, secant method.

Nonlinear Programming:

Direct search methods: Classification of unconstrained minimization methods, rate of convergence, scaling of design variables, random search methods, univariate methods, pattern directions, Powell’s methods, Simplex method.

Nonlinear Programming: Indirect Search (Descent) Methods:

Gradient of a function, Steepest decent method, Fletcher Reeves method, Newton’s method, Davidson-Fletcher-Powell method.

Integer Programming:

Introduction, Graphical representation, Gomory’s cutting plane method: concept of a cutting plane, Gomory’s method for all-integer programming problems, Bala’s algorithm for zero–one programming, Branch-and-Bound Method.

Course Outcomes:

At the end of the course, the student will be able to:

CO1: Define and use optimization terminology, concepts, and understand how to classify an optimization problem.

CO2: Understand how to classify an optimization problem.

CO3: Apply the mathematical concepts formulate the problem of the systems.

CO4: Analyse the problems for optimal solution using the algorithms.

CO5: Interpret the optimum solution.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbook/s

1 Engineering Optimization Theory and Practice S. S. Rao John Wiley & Sons Fourth Edition 2009

2 Optimisation Concepts and Applications in Engineering A. D. Belegundu, T.R. Chanrupatla, Cambridge University Press 2011

Reference Books

1 Engineering Optimization: Methods and Applications Ravindran, K. M. Ragsdell, and G. V. Reklaitis Wiley, New York 2nd ed. 2006