Course Syllabus

AOE 4084 Engineering Design Optimization (Spring 2019)

Instructor Information

Prof. Canfield, 214 Randolph Hall, 231-5981,

  • Class hours: 1:25PM - 2:15PM MWF, RANDolph 320
  • Office hours: 2:30PM - 4:00PM MWF, RANDolph 214 (or by appointment)

Teaching Assistant: David Sandler, Femoyer 310,

  • Office hours: 10:00AM - 11:00 AM Tuesday, Femoyer 310

1:00 PM - 2:00 PM Thursday, Femoyer 310

Emergency Preparedness

Course Description

Use of mathematical programming methods for engineering design optimization including linear programming, penalty function methods, and gradient projection methods. Applications to minimum weight design, [open-loop optimum control,] machine design, and appropriate design problems from other engineering disciplines.


MATH 2224 Multivariable Calculus


Fourth Edition (2016)
Jasbir Arora

Publisher: Elsevier Academic Press; 4th edition
Hardcover ISBN: 9780128008065
eBook ISBN: 9780128009185

Available digitally from VT:
Online companion materials for students:

Course Objectives

Having successfully completed this course, the student will be able to:

  • Examine the description of an engineering design problem to assess whether the solution may be facilitated by an optimization method.
  • Translate the description of the problem at hand into a formal, mathematical optimization statement suitable for application of one of the established optimization methods.
  • Select a specific optimization technique appropriate to the problem and determine whether to use “off-the-shelf” software or develop a new code.
  • Execute the optimization, recover from execution difficulties, evaluate whether the results appear reasonable, reformulate and re-execute the problem, if necessary.
  • Interpret the results in terms of the original description of the problem.

More specifically, the objectives of this course are for each student to... 

  • Know the definition of parameter optimization.
  • Understand the Karush-Kuhn-Tucker Necessary Conditions for Optimality.
  • Distinguish between various classes of optimization: parameter vs functional, univariate vs. multivariate, linear vs. nonlinear, constrained vs. unconstrained, primal vs. dual, and scalar vs. vector.
  • Comprehend the concepts of design variables, objective and constraint functions, local vs. global optima, direct and indirect methods of optimization, penalty functions, Lagrange multipliers, Lagrangian, optimality criterion, convergence criteria, feasibility, usability, vector optimization, design variable linking, reduced basis and formal approximations, convexity, and duality.
  • Apply non-gradient methods, including genetic algorithms and response surface methods, appropriately to engineering design problems.
  • Demonstrate proficiency in using the computational tools needed to solve numerical optimization problems, including gradient and non-gradient based MATLAB toolboxes.
  • Apply the concepts of numerical optimization to formulate and solve nonlinearly constrained engineering design optimization problems of several variables.

Course Schedule (Syllabus)

Administration, Introduction & Problem Formulation
Graphical Solutions
Analytical Solutions
Optimum Design Concepts, Excel & MATLAB
Linear Programming Problems & Simplex Method
Review & Midterm Test #1
1–5, 8
Midterm Project Presentations
Numerical Methods for Unconstrained Design
Quasi-Newton Methods
Numerical Methods for Constrained Design (CSD)
CSD & Sequential Quadratic Programming (SQP)
Multiobjective Optimization
Discrete Variable Optimization
Genetic Algorithms & Test #2 16
Final Project Presentations

Administrative dates and information for this class are provided by the Office of the Registrar:


Grading Policy

 Homework & Class Participation
 In-Class Test 1
 In-Class Test 2
 Final Project

Tests will be graded on a standard numeric scale. If the mean is below a C, then scaled T-scores* will be used to determine letter grade for the test.

Grading Scale
 A  >= 93
 A–  >= 90
 B+  >= 87
 B  >= 83
 B–  >= 80
 C+  >= 77
 C  >= 73
 C–  >= 70
 D+  >= 67
 D  >= 63
 D–  >= 60
 F  >= 0

Each homework problem and the final project will be graded on the following letter grade scale. The homework letter grades will be converted to a numeric score, according the the course grading scale.

Homework Grading Scale
A Correct Answer and Method
B Correct Method
C Nice Try
D No Clue
F No Attempt

Homework may be submitted online as a PDF attachment to the Scholar assignment or a printed hard copy may be turned in at the start of the class on the day it is due. For asynchronous online students for whom there may be a time delay in posting the podcast the HW assignment is due at the start of the following class day. Students are encouraged to discuss homework problems with one another and may compare approach and results, but they are expected to turn in their own, individual work. Do not share computer code. Submit only assignments that are your own work.

Class participation credit will be earned primarily by responding to Socrative exit tickets, as well individual interaction during class (or email or telephone interaction for online students). 

The final project grade will be based on equally weighted midterm and final class presentations and a written report, each graded according to a rubric that will be provided.

*The article, Testing Memo 6: What kind of Grades Should be Averaged?, explains T-scores.

Honor System

Students shall work independently on tests and projects and submit only their own work. Students are permitted to discuss homework problems in groups, but they are expected to turn in their own, individual work. Computer programming code may not be shared, copied, or distributed among students before an assignment is due.

Student and instructor behavior in this class is governed by the Virginia Tech Honor Code and its core values:

  • Mutual Trust
  • Intellectual Honesty
  • Honesty and Integrity promote quest for Truth
All assignments submitted shall be considered graded work and shall be completed on an individual basis unless otherwise stated. While discussing assignments and getting help outside of class is both authorized and encouraged, copying solutions from any source is considered a violation, as is sharing or re-use of a computer file in full or in part. Honesty in your academic work will develop into professional integrity. The faculty and students of Virginia Tech will not tolerate academic dishonesty. It is your responsibility to seek clarification, if there is a question about how the Honor Code applies to a given assignment. Suspected violations of the Honor Code will be processed and dealt with as recommended by the Honor Court.

Policy for Making Up Work

Requests to make up for a missed test or assignment must be made by notifying the instructor in advance of the scheduled due date. Requests due to absences shall be documented through the the Dean of Students, who can verify your absence and notify all of your instructors at once. In case of absences for health reasons, Schiffert Health Center medical staff can verify that you have been given medical treatment. For family or personal emergencies, students should consult with Dean of Students Office, who will notify the Associate Dean of Academic Affairs for Engineering. Circumstances out of the student's control, such as illness, a death in the family, or making a presentation at a professional conference, shall normally be considered an excused absence that justifies the request. Circumstances within the student's control are normally considered an unexcused absence for which a make-up request may be denied.

Unscheduled or undocumented requests will be granted or denied at the discretion of the instructor. The make-up test may be an oral exam.

Students may not discuss with other students a test being made up in between the time the student and the class take the test.

Attendance and Classroom Behavior

Virginia Tech has a class attendance policy. Class meetings are an integral part of most courses and are the central component of many. Students and faculty are expected to attend class at all regularly scheduled times, except for cancellations announced on a university wide basis by the appropriate authority. When students cannot attend a class, it is their responsibility, as soon as possible, to consult with the course instructor about missed work or tests.

Students are expected to respect one another and the instructors in and outside the classroom. Computers may be used in the classroom only for viewing material for this course or for taking notes. Accessing audio, images, or videos during class may be distracting to other students and is strictly prohibited. Cell phone use is prohibited, except as a student response system.

Students with Special Needs

Reasonable and appropriate academic accommodations will be made for students who provide documentation of disability and request for such accommodation.

Please inform the instructor and teaching assistant within the first two weeks of class of potential conflicts that may arise due to participation in religious or ethnic holiday events.

Final Project

The final project report, in lieu of a final exam, will be due on Monday, May 13, 2019 during final exam week.

Course Summary:

Date Details Due