GLPK/FAQ

GNU Linear Programming Kit FAQ

Summary: Frequently Asked Questions about the GNU Linear Programming Kit
Original author: Dr. Harley Mackenzie <hjm@hardsoftware.com>                     

Introduction

Q. What is GLPK?

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 <mao@mai2.rcnet.ru> 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?

A. The GLPK home page is part of the GNU web site and can found at <http://www.gnu.org/software/glpk/glpk.html>.

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 <http://www.gnu.org/prep/ftp.html> 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 <http://gnuwin32.sourceforge.net/packages/glpk.htm>.

Q. Is there a GLPK mailing list or newsgroup?

A. GLPK has two mailing lists: <help-glpk@gnu.org> and <bug-glpk@gnu.org>.

The main discussion list is <help-glpk@gnu.org>, 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 <bug-glpk@gnu.org>.

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 <help-glpk-request@gnu.org> 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 <http://mail.gnu.org/mailman/listinfo/help-glpk> and <http://mail.gnu.org/mailman/listinfo/bug-glpk>.

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 <hjm@hardsoftware.com> 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 <hjm@hardsoftware.com> 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?

A. The latest version of the GLPK FAQ is available to download from <http://www.hardsoftware.com/downloads.php#GLPK+FAQ> 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 <http://plato.asu.edu/bench.html>.

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 <http://users.iems.nwu.edu/~4er/WRITINGS/amplmod.pdf>.

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 <http://gottfried.lindner.bei.t-online.de/glpk.htm>.

There is a Python interface to the LP solver of GLPK available from CVXOPT, see <http://abel.ee.ucla.edu/cvxopt/>

There are other language interfaces under development, including a Perl interface currently being developed by the FAQ maintainer, Dr. Harley Mackenzie <hjm@hardsoftware.com>.

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 <bug-glpk@gnu.org>.

Q. How do I contribute to the GLPK development?

A. At present new GLPK development patches should be emailed to Andrew Makhorin <mao@mai2.rcnet.ru >, 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 <http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html> 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. 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 <http://mail.gnu.org/archive/html/help-glpk/2003-09/msg00017.html>.

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.

Caution: this answer is stale — lpx_simplex() and lpx_integer() have been depreciated, try glp_iotopt() instead.

Q. What are cuts and how do they work?

A. Imagine that you have a MIP instance. Dropping integrality constraints gives you an LP relaxation of the MIP. The feasible set of the LP relaxation is a polyhedron P, whose vertices correspond to basic solutions, which may be non-integral (since integrality constraints are dropped). Now imagine that you construct a convex hull T of the feasible set of the MIP. It is also a polyhedron (called the MIP polytope); by definition every vertex corresponds to a basic solution, which is integral. It is obvious that T is a subset of P. Note that the description of T, i.e. the system of linear inequalities that defines it, is generally unknown. If you find an optimal solution to the LP relaxation, i.e. an optimal vertex of P, say x, and x is non-integral, there must exist a hyperplane called a cutting plane or cut, which cuts off (separates) x from T. If you find some cut ax >= b, you can add this inequality (called valid inequality) to the original MIP; note that if an inequality is valid, every integral solution satisfies it, i.e. it keeps T. Ideally a cut should be a facet of T, however, for many MIP classes it is hard to find such facet-inducing valid inequalities.

Historically the first class of cutting planes was proposed by Ralph Gomory. The branch-and-cut method is the branch-and-bound method, where sub-problems are strengthen with cutting planes, that allows reducing the size of the search tree. On the internet you can find a lot of reports, papers, and books dedicated to the branch-and-cut method.

GLPK database access

Q. Is it possible to read a simple scalar parameter from Access DB via ODBC?

A. Scalar parameters are not allowed in the table statements. However, you can define an array of scalar parameters, e.g.

  set N; /* parameter names */
  param p{N}; /* parameter values */

read S and p{S} from a table, and then use p["test"] in the model.