GLPK (GNU Linear Programming Kit)

GLPK (GNU Linear Programming Kit)
Name	GLPK
Developer	Free Software Foundation
Released	1987
Latest release	4.65
Operating system	Unix-like; Microsoft Windows
Genre	Mathematical optimization
License	GNU General Public License

GLPK (GNU Linear Programming Kit) GLPK is a software package for solving large-scale linear programming and mixed integer programming problems. It provides a standalone solver and a modeling language aimed at researchers and practitioners in operations research, supply chain management, telecommunications, and energy industry. The project is distributed under the GNU General Public License and maintained within the ecosystem associated with the Free Software Foundation and contributors from academic institutions such as Massachusetts Institute of Technology and Universität Wien.

Overview

GLPK implements algorithms for solving linear programs and mixed integer programs using classical methods developed in the literature of mathematical optimization and operations research. Its primary algorithmic heritage traces to techniques described by scholars at Bell Labs, IBM Research, and textbooks by authors affiliated with Stanford University and Princeton University. Because GLPK is written in C (programming language), it can be compiled on Linux, FreeBSD, NetBSD, and Microsoft Windows platforms and integrated with projects from GNU Project, Debian, Red Hat, and openSUSE distributions.

Features and Capabilities

GLPK offers a suite of capabilities commonly required in industrial and academic workflows: an implementation of the revised simplex method influenced by work at Hewlett-Packard and Bell Labs, a primal-dual interior point method akin to algorithms from University of California, Berkeley research groups, and a branch-and-cut integer solver reflecting strategies used at INRIA and ETH Zurich. It supports problem input in the MathProg modeling language, an algebraic modeling dialect inspired by AMPL and used in studies at Cornell University and University of Minnesota. GLPK exposes presolve techniques, basis recovery, and sensitivity analysis features comparable to facilities in commercial solvers from Gurobi and CPLEX as demonstrated in comparative evaluations by researchers at University of Oxford and Imperial College London.

Architecture and Implementation

The core of GLPK is implemented in portable C (programming language) and organized into modules corresponding to matrix storage, simplex tableau operations, factorization routines, and the branch-and-cut framework. Its sparse matrix code draws on methods popularized by researchers at Sandia National Laboratories and Lawrence Livermore National Laboratory, while its LU factorization and numerical stability strategies follow work published by teams at Argonne National Laboratory and University of Illinois Urbana-Champaign. GLPK’s branch-and-cut node management and cut generation modules reflect algorithmic patterns found in software from Zuse Institute Berlin and Siemens AG research labs. The project maintains test suites and benchmarks used in comparisons at INRIA and National Institute of Standards and Technology.

Interfaces and Language Bindings

GLPK ships with a command-line solver and a native MathProg modeling front end, and it provides a C API enabling bindings to high-level languages and systems such as Python (programming language), Julia (programming language), GNU R, Octave, and integration layers used in Apache-based analytics stacks. Community projects have produced wrappers connecting GLPK to environments associated with Microsoft Excel, Jupyter Notebook, and MATLAB interop initiatives from MathWorks. Bindings and packaging efforts have been coordinated alongside distributions like Debian and Homebrew and interfaced in academic pipelines at University of Cambridge and Carnegie Mellon University.

Performance and Use Cases

GLPK is widely used where robust, open-source solvers are preferred for teaching, prototyping, and production tasks in organizations such as World Bank, United Nations, NASA, and small to medium enterprises in manufacturing and transportation planning. Performance evaluations by research groups at ETH Zurich, Delft University of Technology, and Technical University of Munich show that GLPK is competitive for modest-sized models but generally trails high-performance commercial solvers like IBM ILOG CPLEX, Gurobi Optimization, and FICO Xpress on very large, tightly constrained instances. Its deterministic licensing and transparent implementation make it attractive for reproducible research in collaborations involving European Commission projects and public sector studies at agencies such as U.S. Department of Energy.

Licensing and Development History

GLPK was initially developed by contributors associated with the Free Software Foundation and later received maintenance and enhancements from academics and industry engineers affiliated with University of Waterloo, National University of Singapore, and independent contributors worldwide. Distributed under the GNU General Public License, GLPK’s source code and issue tracking have been hosted in repositories following practices used by projects at GNU Project and mirrored in archives connected to SourceForge and modern GitHub workflows. Over its history GLPK has been cited in publications originating from Princeton University, Yale University, and University of California, Los Angeles, reflecting its role in the open-source optimization landscape.

Category:Optimization software