ME 6103: Optimization In Engineering Design

ME 6103: Optimization In Engineering Design
Offered Fall, Even Years

Credit hours:	3-0-3
Prerequisites:	Graduate standing in engineering or related discipline
Catalog Description:	Use of single and multi-objective optimization in modeling and solving mechanical engineering design problems. Formulations, solution algorithms, validation and verification, computer implementation. Project.
Textbooks:	Ashok D. Belegundu, Tirupathi R. Chandrupatla, Optimization Concepts and Applications in Engineering, Pearson Education, 1998.
Instructor::	Bert Bras (Fall 2004)

References:

Ignizio, J. P., 1982, Linear Programming in Single and Multi-Objective Systems, Prentice-Hall, Englewood Cliffs, New Jersey.
Luenberger, D. G., 1984, Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts.

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 computer-based optimization techniques. The students will get a fundamental introduction to optimization techniques which they can augment by taking other courses from ISyE.

Prerequisites by topics:

Topics:

Context:

Operational and Operations Research history; Optimization in context of other decision support tools.; OR models in design and manufacturing; Computer-based solution tools; 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.
DFX Models: Modeling product performance and efficiency; Reliability models; Cost models; Environmental models; Quality and robustness models; Quantifying manufacturability
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; Multiplex algorithms; Sensitivity analyses; Network, transportation, and scheduling problems
Non-Linear optimization models and solution algorithms: General scheme, zeroeth order, first order, second order; Sensitivity analyses and validation; 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: Integrating simulation in optimization models; Multidisciplinary optimization; FEA optimization; Stochastic optimization; Robustness and tolerance optimization
Course Grading:: Homework/Assignments: 60%; Project: 40%
Delivery mode (%):: Lecture 90%; Discussion 10%

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Revised July 2004