Simon Fraser University
Engaging the World

Course Outlines

Fall 2018 - MATH 408 D100

Discrete Optimization (3)

Class Number: 4441

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2018: Mon, Wed, Fri, 9:30–10:20 a.m.
    Surrey

  • Exam Times + Location:

    Dec 12, 2018
    Wed, 12:00–3:00 p.m.
    Surrey

  • Prerequisites:

    MATH 308.

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.

The 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

  • Homework 20%
  • Midterm 30%
  • Final 50%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

Materials

REQUIRED READING:

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

Note: this text is available as an e-text at the SFU Library. Hardcopies of the text will also be available for purchase at the SFU Bookstore. The 2014 and the 2016 versions are the same except for the ISBN.
ISBN: 9783319384320

Registrar Notes:

SFU’s Academic Integrity web site http://students.sfu.ca/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

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS