GNU Linear Programming Kit FAQ
Summary: Frequently Asked Questions about the GNU Linear Programming Kit
Author: Dr. Harley Mackenzie
Posting-Frequency: Monthly
Language: English
$Date: 2004/01/09 05:57:57 $
$Revision: 1.6 $
Introduction
Q. What is GPLK?
A. GLPK stands for the GNU Linear Programming Kit. The GLPK package is
a set of routines written in ANSI C and organized in the form of a
callable library. This package is intended for solving large-scale
linear programming (LP), mixed integer linear programming (MIP), and
other related problems.
The GLPK package includes the following main components:
* implementation of the simplex method,
* implementation of the primal-dual interior point method,
* implementation of the branch-and-bound method,
* application program interface (API),
* GNU MathProg modeling language (a subset of AMPL),
* GLPSOL, a stand-alone LP/MIP solver.
Q. Who develops and maintains GLPK?
A. GLPK is currently developed and maintained by Andrew Makhorin,
Department for Applied Informatics, Moscow Aviation Institute, Moscow,
Russia. Andrew's email address is and his postal
address is 125871, Russia, Moscow, Volokolamskoye sh., 4, Moscow
Aviation Institute, Andrew O. Makhorin
Q. How is GLPK licensed?
A. GLPK is currently licensed under the GNU General Public License
(GPL). GLPK is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version.
GLPK is not licensed under the Lesser General Public License (LGPL) as
distinct from other free LP codes such as lp_solve. The most
significant implication is that code that is linked to the GLPK library
must be released under the GPL, whereas with the LGPL, code linked to
the library does not have to be released under the same license.
Q. Where is the GLPK home page?
The GLPK home page is part of the GNU web site and can found at
.
Q. How do I download and install GLPK?
A. The GLPK source distribution can be found in the subdirectory
/gnu/glpk/ on your favorite GNU mirror
and can be compiled directly from
the source.
The GLPK package (like all other GNU software) is distributed in the
form of packed archive. This is one file named 'glpk-x.y.tar.gz', where
x is the major version number and y is the minor version number.
In order to prepare the distribution for installation you should:
1. Copy the GLPK distribution file to some subdirectory.
2. Enter the command 'gzip -d glpk-x.y.tar.gz' in order to unpack the
distribution file. After unpacking the name of the distribution file
will be automatically changed to 'glpk-x.y.tar'.
3. Enter the command 'tar -x < glpk-x.y.tar' in order to unarchive the
distribution. After this operation the subdirectory 'glpk-x.y' which is
the GLPK distribution will have been automatically created.
After you have unpacked and unarchived GLPK distribution you should
configure the package, and compiled the application. The result of
compilation is:
* the file 'libglpk.a', which is a library archive containing object code
for all GLPK routines; and
* the program 'glpsol', which is a stand-alone LP/MIP solver.
Complete compilation and installation instructions are included in the
INSTALL file included with the distribution.
The distribution includes make files for the Microsoft Visual C/C++
version 6 and Borland C/C++ version 5 and by default compiles and links
a glpk*.lib library file, a glpk*.dll DLL file and an glpsol.exe
application file. A GNU Windows 4.1 binary, source and documentation
compiled using the mingw32 C/C++ compiler is also available from
.
Q. Is there a GLPK mailing list or newsgroup?
A. GLPK has two mailing lists: and
.
The main discussion list is , and is used to discuss
all aspects of GLPK, including its development and porting. There is
also a special list used for reporting bugs at .
To subscribe to any GLPK mailing list, send an empty mail with a
Subject: header line of just "subscribe" to the relevant -request list.
For example, to subscribe yourself to the main list, you would send
mail to with no body and a Subject: header
line of just "subscribe".
Another way to subscribe to the GLP mailing lists is to visit the web
pages and
.
Currently there are no newsgroups dedicated to GLPK.
Q. Who maintains this FAQ and how do I contribute to this FAQ?
A. The present maintainer of this FAQ is Dr. Harley Mackenzie, HARD
software, although the content of the FAQ is derived from many sources
such as GLPK documentation, GLPK email archives and original content.
Harley's email address is and his postal address
is c/o HARD software, PO Box 8004, Newtown, Victoria 3220, Australia.
All contributions to this FAQ, such as questions and (preferably)
answers should be sent to the email address.
This FAQ is copyright Harley Mackenzie 2003 and is released under the
same license, terms and conditions as GLPK, that is, GPL version 2 or
later.
Contributions are not directly referenced in the body of the FAQ as
this would become unmanageable and messy, but rather as a list of
contributors to this FAQ. If you are the author of any information
included in this FAQ and you do not want your content to be included,
please contact the FAQ maintainer and your material will be removed.
Also if you have not been correctly included as a contributor to this
FAQ, your details have changed, or you do not want your name listed in
the list of contributors, please contact the FAQ maintainer for
correction.
Q. Where can I download this FAQ?
The latest version of the GLPK FAQ is available to download from
in the following
formats:
* DocBook
* Formatted text
* Adobe PDF
Q. Who are the FAQ contributors?
A. The FAQ contents were created from the following sources:
* Michael Hennebry
* http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html
* Harley Mackenzie, HARD software Pty. Ltd.
* Andrew Makhorin, Department for Applied Informatics, Moscow Aviation
Institute
GLPK functions & features
Q. What is the current state of GLPK development?
A. GLPK is a work in progress and is presently under continual
development. As of the current version 4.3, GLPK is a simplex-based
solver is able to handle problems with up to 100,000 constraints. In
particular, it successfully solves all instances from netlib (see the
file bench.txt included in the GLPK distribution). The interior-point
solver is not very robust as it is unable to handle dense columns,
sometimes terminates due to numeric instability or slow convergence.
The Mixed Integer Programming (MIP) solver currently is based on
branch-and-bound, so it is unable to solve hard or very large problems
with a probable practical limit of 100-200 integer variables. However,
sometimes it is able to solve larger problems of up to 1000 integer
variables, although the size that depends on properties of particular
problem.
Q. How does GLPK compare with other LP codes?
A. I think that on very large-scale instances CPLEX 8.0 dual simplex is
10-100 times faster than the GLPK simplex solver and, of course, much
more robust. In many cases GLPK is faster and more robust than lp_solve
4.0 for pure LPs as well as MIP's. See the bench.txt file in the GLPK
distribution doc directory for GLPK netlib benchmark results.
You can find benchmarks for some LP and MIP solvers such as CPLEX,
GLPK, lp_solve, and OSL on Hans Mittelmann's webpage at
.
Q. What are the differences between AMPL and GNU MathProg?
A. The subset of AMPL implemented in MathProg approximately corresponds
to AMPL status in 1990, because it is mainly based on the paper Robert
Fourer, David M Gay and Brian W Kernighan (1990), "A Modeling Language
for Mathematical Programming", Management Science, Vol 36, pp. 519-554
and is available at
.
The GNU MathProg translator was developed as part of GLPK. However, GNU
MathProg can be easily used in other applications as there is a set of
MathProg interface routines designed for use in other applications.
Q. What input file formats does GLPK support?
A. GLPK presently can read input and output LP model files in three
supported formats:
* MPS format - which is a column oriented and widely supported file
format but has poor human readability.
* CPLEX format - which is an easily readable row oriented format.
* GNU MathProg - which is an AMPL like mathematical modeling language.
Q. What interfaces are available for GLPK?
A. The GLPK package is in fact a C API that can be either by statically
or dynamically linked directly with many programming systems.
Presently there are three contributed external interfaces included with
the GLPK package:
* GLPK Java Native Interface (JNI)
* GLPK Delphi Interface (DELI)
* GLPKMEX Matlab MEX interface
There is an unofficial Microsoft Visual Basic, Tcl/Tk and Java GLPK
interface available at
.
There are other language interfaces under development, including a Perl
interface currently being developed by the FAQ maintainer, Dr. Harley
Mackenzie .
Q. Where can I find some examples?
A. The GLPK package distribution contains many examples written in GNU
MathProg (*.mod), C API calls (*.c), CPLEX input file format (*.lpt),
MPS format (*.mps) as well as some specific Traveling Salesman examples
(*.tsp).
All of the examples can be found in the GLPK distribution examples
sub-directory.
Q. What are the future plans for GLPK?
A. Developments planned for GLPK include improving the existing key
GLPK components, such as developing a more robust and more efficient
implementation of the simplex-based and interior-point solvers. Future
GLPK enhancements planned are implementing a branch-and-cut solver, a
MIP pre-processor, post-optimal and sensitivity analysis and possibly
network simplex and quadratic programming solvers.
Q. How do I report a GLPK bug?
A. If you think you have found a bug in GLPK, then you should send as
complete a report as possible to .
Q. How do I contribute to the GLPK development?
A. At present new GLPK development patches should be emailed to Andrew
Makhorin , with sufficient documentation and test
code to explain the nature of the patch, how to install it and the
implications of its use. Before commencing any major GLPK development
for inclusion in the GLPK distribution, it would be a good idea to
discuss the idea on the GLPK mailing list.
Q. How do I compile and link a GLPK application on a UNIX platform?
A. To compile a GLPK application on a UNIX platform, then compiler must
be able to include the GLPK include files and link to the GLPK library.
For example, on a system where the GLPK system is installed:
gcc mylp.c -o mylp -lglpk
or specify the include files and libglpk.a explicitly, if GLPK is not
installed.
Q. How do I compile and link a GLPK application on a Win32 platform?
A. On a Win32 platform, GLPK is implemented either as a Win32 Dynamic
Link Library (DLL) or can be statically linked to the glpk*.lib file.
As with the UNIX instructions, a GLPK application must set a path to
the GLPK include files and also reference the GLPK library if
statically linked.
Q. How do I limit the GLPK execution time?
A. You can limit the computing time by setting the control parameter
LPX_K_TMLIM via the API routine lpx_set_real_parm . At present there is
no way of limiting the execution time of glpsol without changing the
source and recompiling a specific version.
GLPK Linear Programming
Q. What is Linear Programming and how does it work?
A. Linear Programming is a mathematical technique that is a generic
method for solving certain systems of equations with linear terms. The
real power of LP's are that they have many practical applications and
have proven to be a powerful and robust tool.
The best single source of information on LP's is the Linear Programming
FAQ
that has information on LP's and MIP's, includes a comprehensive list
of available LP software and has many LP references for further study.
Q. How do I determine the stability of an LP solution?
A. You can perform sensitivity analysis by specifying the --bounds
option for glpsol as:
glpsol ... --bounds filename
in which case the solver writes results of the analysis to the
specified filename in plain text format. The corresponding API routine
is lpx_print_sens_bnds() .
Q. How do I determine which constraints are causing infeasibility?
A straightforward way to find such a set of constraints is to drop
constraints one at a time. If dropping a constraint results in a
solvable problem, pick it up and go on to the next constraint. After
applying phase 1 to an infeasible problem, all basic satisfied
constraints may be dropped.
If the problem has a feasible dual, then running the dual simplex
method is a more direct approach. After the last pivot, the nonbasic
constraints and one of the violated constraints will constitute a
minimal set. The GLPK simplex table routines will allow you to pick a
correct constraint from the violated ones.
Note that the GLPK pre-solver needs to be turned off for the preceding
technique to work, otherwise GLPK does not keep the basis of an
infeasible solution.
Also a more detailed methodology has been posted on the mail list
archive at
.
Q. What is the difference between checks and constraints?
A. Check statements are intended to check that all data specified by
the user of the model are correct, mainly in the data section of a
MathProg model. For example, if some parameter means the number of
nodes in a network, it must be positive integer, that is just the
condition to be checked in the check statement (although in this case
such condition may be also checked directly in the parameter
statement). Note that check statements are performed when the
translator is generating the model, so they cannot include variables.
Constraints are conditions that are expressed in terms of variables and
resolved by the solver after the model has been completely generated.
If all data specified in the model are correct a priori, check
statements are not needed and can be omitted, while constraints are
essential components of the model and therefore cannot be omitted.
GLPK Integer Programming
Q. What is Integer Programming and how does it work?
A. Integer LP models are ones whose variables are constrained to take
integer or whole number (as opposed to fractional) values. It may not
be obvious that integer programming is a very much harder problem than
ordinary linear programming, but that is nonetheless the case, in both
theory and practice.
Q. What is the Integer Optimization Suite (IOS)?
A. IOS is a framework to implement implicit enumeration methods based
on LP relaxation (like branch-and-bound and branch-and-cut). Currently
IOS includes only basic features (the enumeration tree, API routines,
and the driver) and is not completely documented.
Q. I have just changed an LP to a MIP and now it doesn't work?
A. If you have an existing LP that is working and you change to an MIP
and receive a "lpx_integer: optimal solution of LP relaxation required"
204 (==LPX_E_FAULT) error, you probably have not called the LP solution
method lpx_simplex() before lpx_integer() . The MIP routines use the LP
solution as part of the MIP solution methodology.