Simon Fraser University
Engaging the World

Course Outlines

Fall 2024 - MATH 408 D100

Discrete Optimization (3)

Class Number: 3957

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2024: Mon, 2:30–4:20 p.m.
    Surrey

    Oct 15, 2024: Tue, 2:30–4:20 p.m.
    Surrey

    Sep 4 – Dec 3, 2024: Wed, 2:30–3:20 p.m.
    Surrey

  • Exam Times + Location:

    Dec 6, 2024
    Fri, 3:30–6:30 p.m.
    Surrey

  • Prerequisites:

    MATH 308 with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

Model building using integer variables, computer solution, relaxations and lower bounds, heuristics and upper bounds, branch and bound algorithms, cutting plane algorithms, valid inequalities and facets, branch and cut algorithms, Lagrangian duality, column generation of algorithms, heuristics algorithms and analysis. Quantitative.

COURSE DETAILS:

Model building using integer, binary and mixed integer variables.  Computer solution of integer programming models, linear programming relaxations, duality, simple upper bounds using greedy algorithms.  Branch and bound algorithms, implicit enumeration, LP based branch and bound.

Valid inequalities, Gomory's fractional cut, mixed integer cuts, strong valid inequalities, simple facets for the 0-1 knapsack polytope and the traveling salesman polytope, branch and cut algorithms.

Lagrangian relaxation, strength of the Lagrangian dual, Lagrangian heuristics.

Column generation algorithm, solving the symmetric traveling salesman problem using column generation.

Greedy and local search algorithms, construction heuristics, worst case analysis of heuristics.

Grading

  • Individual assignments 40%
  • Team assignments 20%
  • Midterm 15%
  • Final 25%

REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

Materials

REQUIRED READING:

Integer Programming
Zambelli, G. Conforti, M. and Cornuejols, G.
Springer, 2016

Online access to this text via the SFU library: 

https://sfu-primo.hosted.exlibrisgroup.com/permalink/f/1u29dis/TN_springer_s978-3-319-11008-0_326714

The 2014 and the 2016 versions are the same except for the ISBN.
ISBN: 9783319384320

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.