ME 609 : Optimization Methods in Engineering

ME 609 : Optimization Methods in Engineering

Instructor : Narayan Rangaraj (narayan@iitg.ernet.in)

TAs for the course : D. N. Vadiraja (vadiraja@iitg.ernet.in)

J.S.Rao (jsrao@iitg.ernet.in)

Course timings : Mon 9.00 a.m., Tue 8.00 a.m. and Thu 8.00 a.m.

Venue : Classroom H-1, Academic complex

The course will cover a mix of modeling, theory, algorithms and numerical methods, as per the interests and background of the class. The objective of the course is to familiarize the student with the principles of formulation and solution of optimization problems in engineering and provide the mathematical background to understand and design algorithms for their solution.

Course contents (35 hours):

Introduction to optimization (formulation and mathematical background) – 3 lectures

Classical methods of optimization based on calculus of functions of several variables – 9 lectures

Single variable optimization – self study

Optimality conditions (First order and second order necessary and sufficient conditions)

Steepest descent, Newton and Quasi Newton Methods

Trust region methods – [if time permits]

Linear programming – 9 lectures

Simplex method – revision and self study

Intro to Ellipsoid and Interior Point methods – [if time permits]

Duality and Sensitivity

Network flow LPs

Constrained optimization – 6 lectures

Kuhn Tucker conditions

Quadratic Programming

Sequential Quadratic Programming (Lagrange Newton methods)

Integer programming – 3 lectures

Integer programming formulations and examples

IP through LP relaxation

Branch and bound

Nontraditional optimization – 5 lectures

Simulated annealing

Lagrangean relaxation

Genetic algorithms – [if time permits]

Class text – Optimization Concepts and Applications in Engineering, Ashok D. Belegundu and Tirupathi R. Chandrupatla, Pearson Education, Delhi, 1999

Supplementary texts –

For LP - Linear Programming and Network Flows, [2^nd edition], M.S.Bazaraa, J.J.Jarvis and H.D.Sherali, Wiley, 1990 or Operations Research, H. Taha

For non-traditional optimization - Modern Heuristics for Combinatorial Optimization, C. Reeves, Orient Longman, 1993

For Engineering Applications – Optimization for Engineering Design : Algorithms and Examples, K. Deb, Prentice Hall India, 1995

Mathematical Background – Introduction to Optimization, Edwin K.P.Chong and S.H.Zak

General Background, Geometric Programming, etc. – Optimization: Theory and Applications, S.S.Rao, Wiley Eastern, 1984

Evaluation scheme :

Final exam : 40% weightage

Mid term exam : 20%

4 Quizzes : 10% each Dates of the quizzes will be announced later.

2 quizzes 10% each and an independent project will be evaluated for 20 %.

Guidelines for independent project: The project can be done independently, or in groups of 2 (evaluation will be joint, but there could be a brief viva with either student in a group). The project has to do with either (a) a modeling and analysis of an optimization formulation to some engineering problem, or (b) development of code for an identified algorithm and demonstrating it. In either case, a one page write up on the course project has to be submitted, which will be approved by the instructor/TAs. Last date for giving the one page write ups – Monday 27-2-2006 5 p.m. in the department office. Approval given by 6-3-2006 (latest). The earlier you give your proposal, the better. Written submission of project by group – 3-4-2006 in the department office.

The project report will be evaluated on clarity of problem definition, proper description of the algorithm or model, presentation of learnings and/or results from the study and proper referencing as appropriate.