COMP 567 Discrete Optimization - II
Please check at least once a
course home page
is posted, due April 30 (absolute deadline!). Submit a pdf file by email to firstname.lastname@example.org
Montreal Industrial Problem solving workshop, August 18-22, 2008 at CRM
To open an account:
Login to any SOCS machine at Trottier 3rd floor
(or McConnell 110) with “newuser” as user name and “newuser” as
Then, follow the
instructions to open an account.
In the course we make use of the packages cplex and
zimpl, and to some extent maple, lp_solve, cplex
and lrs. All are installed on lab
machines in Trottier: labi-j.cs.mcgill.ca,
1<=i<=9 and 1<=j<=30 (Try
i= 6 first).
You can connect remotely by ssh: eg: ssh
(if it does not work, try rebooting the local machine:
ctrl+alt+F1 -> ctrl+alt+delete )
A full list of machine names in labs is here: http://www.cs.mcgill.ca/socsinfo/labs/
If you do not find the software, try typing: %source
You will need to set the path for some of the software.
cplex path: /usr/local/bin/cplex-10
cplex-10 gives you the
cplex command line prompt
Instructions for cplex can be found here
(It may be necessary to set an environment variable, see instructions
[options] file ...
modelling tool for LPs and ILPs (constraint
generator to lp or mps formats).
It is easy to learn and use. On page 16 of the documentation
you will find Chvatal's
diet problem as an example.
maple path: /usr/local/bin/maple
A maple session that shows how to solve systems of equations is here.
This program can be used to solve linear or integer linear programs.
Usage: lp_solve -S4 <
input_file (-S4 option gives dual
Some examples input and output files are here.
The man page is here.
The full package is available for download from the lp_solve home
A nice help page with windows executable is available at:
This program computes all of the extreme points (and extreme rays if
any) of the
feasible region of an LP. Home page is: http://cgm.cs.mcgill.ca/~avis/C/lrs.html
Infrastructure for Operations Research
-->"an open-source community for operations research software in
to speed development and deployment of models, algorithms, and
computational research." It has some neat cut generators for solving
source Mixed ILP solver that implements branch and cut
-->it s very customizable and is part of COIN-OR. If you tweak things
right, you will solve tough ILPs faster than CPLEX can. You can even
implement your own cuts.
Here is some information on some alternate texts:
Integer Programming and Combinatorial Optimization , W. Cook et
A recent book with lots of very nice proofs and material
supplemental to what we will be studying.
Combinatorial Optimization, Papadimitriou and Steiglitz, 1982
Despite its age, one of the best all round books on LP, ILP,
Combinatorial Optimization and Complexity.
Integer and Combinatorial Optimization, Nemhauser and Wolsey, 1988,
The revised version (paperback) is similar to the
original, which is a good solid theoretical study
of IP and CO. Lots of examples and exercises.
Combinatorial Optimization, A. Schijver, 2003
Box set, 3 volumes, 1800 pages all for $140. A tour de force,
but covers mostly the polynomial time side of the subject which we are
not emphasizing in 567.
Theory of Linear and Integer Programming, A. Schrijver, 1986
Very dense and comprehensive, best as a reference book.
I have all these in my office if you would like to take a