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IUPUI School of Engineering and Technology

IUPUI School of Engineering and Technology

Design Optimization Methods

ME 59700 / 3 Cr. (3 Class)

In this course, the general theory of optimization, concepts and problem statement are presented. Methods for minimization of a function of one or n variables with and without constraints are discussed. Response surface methods and design of experiments are shown to significantly reduce analysis time. Applications using a commercial software package to solve typical engineering design optimization problems are demonstrated. Uncertainty in the design process is introduced. In addition to engineering, the methods studied can be applied to a variety of diverse disciplines such as finance, investment portfolio management, and life sciences.

Textbooks

Numerical Optimization Techniques for Engineering Design, Garret N. Vanderplaats, 3rd Edition with software

Goals

In this course students will acquire the essential knowledge and skills to understand and master the tools and methods for design and optimization of complex engineering problems.

Outcomes

After completion of this course, the students should be able to:

  1. Explain the concept of the existence and uniqueness of an optimal solution [a, e]
  2. Understand basic optimization methods for a single variable [a, e, k]
  3. Understand the use of applying various type of constraints to numerical optimization [a, e, k4]
  4. Apply response surface methods to model complex engineering systems [a, e, k]
  5. Apply design of experiments techniques to model a design space [a, e, k]
  6. Solve numerical optimization problems of n-variables with constraints [a, k]
  7. Use of a practical software package to solve typical engineering problems [a, e, k]
  8. Model a realistic engineering design optimization problem as a semester project [a, c, d, e, f, g, h, i, j, k]

Note: The letters within the brackets indicate the general program outcomes of mechanical engineering. See: ME Program Outcomes.

Topics
  1. Introduction/Overview
  2. Review of Basic Calculus Concepts I
  3. Review of Basic Calculus Concepts II
  4. Review of Basic Calculus Concepts III
  5. Optimization Concepts and General Problem Statement
  6. Existence and Uniqueness of an Optimal Solution
  7. Standard Linear Programming Form
  8. The SIMPLEX Method
  9. Polynomial Approximations
  10. Golden Section Method
  11. Constrained Functions of One Variable
  12. General Strategy for Minimizing Functions of One Variable
  13. Zero-Order Methods
  14. First-Order Methods
  15. Second-Order Methods
  16. Scaling and Convergence Criteria
  17. Isight Design/Optimization Software
  18. Exterior Penalty Function Method
  19. Interior Penalty Function Method
  20. Augmented LaGrange Multiplier Method
  21. Design Variable Linking and Reduced Basis Concept
  22. Response Surface Methods I
  23. Response Surface Methods II
  24. Design of Experiments I
  25. Design of Experiments II
  26. Random Search, Genetic Search
  27. Sequential Linear Programming
  28. Multi-objective Design
  29. Six Sigma Design (Uncertainty in Design)
Computer Usage
Student use MATLAB for some HW problems.