### Design Optimization Methods

#### ME 50601 / 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.

**Available Online:** No

**Credit by Exam:** No

**Laptop required:** No

**Prerequisites/Co-requisites:**

P: MATH 26600 and MATH 26100

##### 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:**

- Explain the concept of the existence and uniqueness of an optimal solution [a, e]
- Understand basic optimization methods for a single variable [a, e, k]
- Understand the use of applying various type of constraints to numerical optimization [a, e, k4]
- Apply response surface methods to model complex engineering systems [a, e, k]
- Apply design of experiments techniques to model a design space [a, e, k]
- Solve numerical optimization problems of n-variables with constraints [a, k]
- Use of a practical software package to solve typical engineering problems [a, e, k]
- 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

- Introduction/Overview
- Review of Basic Calculus Concepts I
- Review of Basic Calculus Concepts II
- Review of Basic Calculus Concepts III
- Optimization Concepts and General Problem Statement
- Existence and Uniqueness of an Optimal Solution
- Standard Linear Programming Form
- The SIMPLEX Method
- Polynomial Approximations
- Golden Section Method
- Constrained Functions of One Variable
- General Strategy for Minimizing Functions of One Variable
- Zero-Order Methods
- First-Order Methods
- Second-Order Methods
- Scaling and Convergence Criteria
- Isight Design/Optimization Software
- Exterior Penalty Function Method
- Interior Penalty Function Method
- Augmented LaGrange Multiplier Method
- Design Variable Linking and Reduced Basis Concept
- Response Surface Methods I
- Response Surface Methods II
- Design of Experiments I
- Design of Experiments II
- Random Search, Genetic Search
- Sequential Linear Programming
- Multi-objective Design
- Six Sigma Design (Uncertainty in Design)