ME 6103 – Optimization in Engineering Design
Instructor:
Bert Bras, Professor, MaRC 253/COM Suite 400.
Tel: 404-894-9667
Catalog Listing: Use of single and multi-objective optimization in modeling and solving
mechanical engineering design problems. Formulations, solution algorithms,
validation and verification, computer implementation.
Credits
3 semester credits. Lecture/discussion 3 hours per week.
Prerequisites
Graduate standing, basic computer programming skills.
Textbook
“Optimization Concepts and Applications in Engineering”, Ashok D.
Belegundu and Tirupathi R. Chandrupatla, Prentice-Hall, NJ, ISBN 0-13031279-7.
Suppl. notes
Additional course notes are to be found on the Systems Realization Laboratory web
server (http://www.srl.gatech.edu) under education and ME6103.
Goals:
To provide Mechanical Engineering students and others interested in engineering design a view
of optimization as a tool for design. The course is designed to provide students with an
opportunity to learn how to model design problems so that they can be solved using computerbased optimization techniques. The students will get a fundamental introduction to optimization
techniques that they can augment by taking other courses from ISyE.
Assessment:
A grade is determined using the following means:
• Written homework, including computer assignments.
• A project with assessment based on technical content, quality, and rigor of modeling,
solution and verification/validation of results, etc.
Dr. Bert Bras
Telephone 404-894-9667
Fax 404-894-7896
E-mail bert.bras@me.gatech.edu
Tentative Topics (subject to change):
Context:
Operational and Operations Research history
Optimization in context of other decision support tools.
OR models in design and manufacturing
Verification and validation.
Single versus Multi-Objective models
Multi-objective formulations (baseline model, goal programming, etc).
Multi-objective solution algorithms.
Converting single objective algorithms into multi-objective algorithms.
Utility theory
Linear models and solution methods
Linear models in design
Simplex theorem, convexity, global and local extrema
Single objective linear models
Simplex algorithm
Multi-Objective linear models and multiplex algorithms
Optimality
Karesh-Kuhn-Tucker Conditions
Pareto Optimality
Sensitivity analyses and validation
Non-Linear optimization models and solution algorithms
General scheme, zeroth order, first order, second order
Use of line searches (bracketing, Golden Section, Newton & False position method)
Multivariate unconstrained problems and algorithms (Newton, Coordinate descent, Conjugate Gradient method)
Constraint Nonlinear Optimization
Difference between constraints, goals and objectives in design
Design problem formulations
Quasi Newton methods, Hessian updates, DFP and BFGS methods
Penalty and Barrier methods
Sequential and Adaptive Linear Programming
Quadratic programming
Primal Methods
Feasible Directions method
Active Set methods
Gradient Projection methods
(Generalized) Reduced Gradient methods
Discrete and mixed integer models
Catalog design
Boolean conversions
Branch & Bound, Cutting Plane methods
Combinatorial explosion
Monte-Carlo methods
Simulated Annealing
Genetic Algorithms
Special Topics: To be determined
Dr. Bert Bras
Telephone 404-894-9667
Fax 404-894-7896
E-mail bert.bras@me.gatech.edu