||Graduate standing in engineering or related discipline
||Use of single and multi-objective optimization in modeling and solving mechanical engineering design problems. Formulations, solution algorithms, validation and verification, computer implementation. Project.
||Ashok D. Belegundu, Tirupathi R. Chandrupatla, Optimization Concepts and Applications in Engineering, Pearson Education, 1998.
||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.
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.
- 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
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