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.
Instructors: Bert Bras
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.

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.

  • 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
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