Design Optimization Methods
ME 50601/ 3 Cr.
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
Instruction Goal
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)
