625.615.83 - Introduction to Optimization

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days starting on WEDNESDAYS, except as noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Optimization Applications
• Formulation of Optimization Models
• Graphical Solution of Linear Programs
• Simplex Method
• Linear Programming Duality and Sensitivity Analysis
• Nonlinear Optimization Theory
• Steepest Descent and Conjugate Gradient Methods
• Newton and Quasi-Newton Methods
• Quadratic Programming
• Network Models
• Dynamic Programming
• Multi-objective Programming
• Optimization Heuristics

Course Goals

This course covers fundamental methods of optimization. Emphasis in this course will be on formulating optimization problems, understanding the methods available to address them, and solving them using appropriate means.

Course Learning Outcomes (CLOs)

• Learn how to convert real world scenarios involving optimization into mathematical problems.
• Use the Simplex Method, and some of its variants to numerically solve problems that can be stated as linear programs.
• Apply classical methods of optimization to problems that may be formulated using nonlinear functions.
• Address special topics such as multi-objective optimization, dynamic programming, non-derivative optimization methods, and optimization heuristics.
• Obtain numerical solutions for a variety of optimization problems using Matlab (or other software as approved by instructor).

Textbooks

Rao, Singiresu S. (2019). Engineering Optimization: Theory and Practice (5th ed.). Hoboken, NJ: John Wiley & Sons, Inc. ISBN-13: 978-1119454717 (optional; the fourth edition is also fine and it is available online from the JHU library.)

Required Software

You will need access to a recent version of MATLAB with the Optimization Toolkit. The MATLAB Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. Instructions on how to obtain access to the software is provided in the Course Information module.

Student Coursework Requirements

It is expected that each module will take approximately 8–11 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2–3 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 2–3 hours per week), and writing assignments (approximately 4–5 hours per week).

Final grades for this course will be determined by the following weighting:

Discussions (10% of Final Grade Calculation)

All modules, except Modules 7 and 14, will have instructor provided discussion questions.  You are responsible for providing an answer to ONE question each week for at least 10 of the 12 discussions.  You should not answer a question already answered by another student unless your approach is significantly different from what has already been provided.  In addition, you are required to respond to your classmates' questions about your solution and provide any additional resources that you believe will be helpful.  You are encouraged to collaborate (within the JHU guidelines on academic integrity) on these assignments but you should write up your own final solution.

Homework Assignments (25% of Final Grade Calculation)

All modules, except Modules 7, 13, and 14, will contain a graded problem set. These assignments will be based on the theory and algorithms discussed in the associated module. Each assignment will have approximately 5 problems of varying difficulty. You are always encouraged to collaborate (within the JHU guidelines on academic integrity) on assignments. This year, you are allowed to work in a group up to size 3 on homework assignments.  If you choose to work in a group, elect one of the group members to be responsible for submitting the assignment for the entire group.

REMINDER: Direct copying of someone else’s work or computer code is considered to be cheating and will result in a grade of zero on the assignment and a possible F in the course.

Usually you will be required to complete a problem “by hand.” This means that you should not use any software or electronic device (save a simple calculator) to do the work. (However there is no reason you cannot check your work with commercially available software, shareware, freeware, etc.) Some assignments will have a computing (Matlab) component that you will also complete individually.

Graded assignments will be returned weekly, providing frequent feedback. Problem sets will be graded out of 100 points. The allocation of those points to specific problems may vary from assignment to assignment depending on the degree of difficulty. 

All problem sets are due according to the dates in the Calendar. No late problem sets will be accepted.  The two lowest homework grades will be dropped (provided that such grades are not the results of violations of academic integrity).

Presentations (5% of Final Grade Calculation)

Exams (60% of Final Grade Calculation, combined from 30% for Midterm and 30% for Final)

There will be two exams given, one in Module 7 and the other in Module 14. Each of these exams will be timed and open book, with no collaboration allowed. The midterm exam (Module 7) will focus on the course material taught in Modules 1-6. The final exam (Module 14) will focus on the course material taught in Modules 8-13.

Both of these exams will provide you the opportunity to demonstrate your ability to determine the required techniques and apply them to solve an optimization problem outside of the framework of a specific lecture/individual topic. Each of these exams will be worth 30% of your final grade

Grading Policy

Individual Item Grading

Partial credit may be given.  For each individual homework and/or exam item that is graded the following (approximate) rubric will be used:

• 100 – 90% of item’s total points: Very good to excellent work; 0-1 minor issues.
• 80 – 89% of item’s total points: Good work however there are some aspects that could be improved; 0-1 major issues and/or 2 or more minor issues.
• 70 – 79% of item’s total points: Satisfactory work. Student shows understanding of what needs to be done but there are multiple issues that need to be addressed; 2-3 major issues.
• 0 – 69% of item’s total points: Unsatisfactory work. (Includes lack of understanding of assignment, extreme carelessness, etc.)

Course Policies

Instructor Comments on Academic Dishonesty

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.  Ignorance of these rules is not an excuse.

• In this course, you may collaborate with other students on homework and/or projects (unless otherwise stated). However, you are ALWAYS to write up your solutions individually, even when you work in a group (again, unless otherwise instructed). 
• Use of previous course material is prohibited (except as provided by the instructor). If you have questions about this policy, please ask the instructor.
• Use of (online) repositories which provide solutions is ALWAYS prohibited.
• Use of solutions manuals and other instructor materials are ALWAYS prohibited.
• Submitting another person's work as your own is ALWAYS prohibited.
• Students are reminded that misrepresenting information about their personal circumstances to a university official, including a faculty member, constitutes academic dishonesty and is grounds for action by the Academic Ethics Board.
• If you are aware of any classmates involved in behavior of questionable ethics with regards to this class, you should contact the instructor immediately.

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.