Global Optimization Software

Global Search, As Timely As Ever

``Consider everything. Keep the good. Avoid evil whenever you notice it.''
(1 Thess. 5:21-22)

This file is part of my global optimization web site. It contains sections on

We are working on a comparative evaluation of a number of currently available constrained global optimization programs. The results will be made publicly available here. If, as an authors of such software, you are interested in our evaluation of your code, the notes on Global Optimization Software Evaluation will tell you what you need to know.

Janos Pintér's recent Optima Newsletter survey on continuous global optimization software is now available online. Please send new or updated information regarding your global optimization software to Janos Pintér.

Below is a list of publicly available global optimization programs (and a few commercial ones). The quality in terms of speed, reliability, and/or automatic parameter choices, stopping tests and ease of use differs widely. I have not checked out the codes (will perhaps be done some day); but I am very interested in comparisons (cf. test results available online) or any other useful comments (mail here) on the sources given.

In a few cases, I added information on problems where a code has difficulties. This is not meant to criticize the code (it may work excellent on other classes of problems) but as a service to the research community: to challenge researchers to overcome current limitations, and to compete for better and better techniques.

Lack of critical information doesn't mean that a code has no problems, but only that nobody informed me about any weaknesses. Indeed, all current global optimization codes for nonlinear problems are unreliable (i.e., cannot always find the global optimum in a reasonable, predictable amount of time and space), with unknown performance limits.

At the present stage of knowledge, if you need global optimization you must experiment with the known methods (or packages) until you have something satisfying you. Unfortunately, this is a rather unsatisfactory state of the art... In general, performance must be expected to deteriorate with increasing dimension. Dimension 50-100 is probably already very high for general-purpose codes on all but the simplest problems. Many codes allow no constraints or only bound constraints.

Since I was asked repeatedly what to try first, here are some suggestions for continuous problems. But they are backed up by little else than my feelings of what I'd try first, and I am using a small font size to emphasize that this is information of a poorer quality than in the rest of my pages. Please write me if you have significant experience that leads to improved suggestions, or that confirms the ones given.

Public Domain Systems

Some Commercial Systems

GloMIQO, Global Mixed-Integer Quadratic Optimizer in GAMS (by Misener and Floudas)
solves quadratically constrained quadratic programs with optional integer constraints to global optimality.

BARON, Branch-And-Reduce Optimization Navigator in Fortran (by Nikos Sahinidis)
A general purpose solver for optimization problems with nonlinear constraints and/or integer variables. Fast specialized solvers for many linearly constrained problems. GAMS interface.

LINDO/LINGO now has global optimization facilities

Interval Global Solver from Frontline Systems. Visual Basic and Excel interfaces

LSGRG Nonlinear Mixed Integer Solver for AMPL

MINOPT (Mixed Integer Nonlinear Programming)

GAMS/DICOPT Solver for Mixed Integer Nonlinear Programming

EZMod Quadratic Mixed Integer Programming (QMIP) Solver

CPLEX Linear Mixed Integer Solver (branch-and-bound for mixed integer linear programs)

CMMIP, Mixed Integer Programming for mixed integer LPs
``In CMMIP, each processor runs a version of CPLEX ... Parallelism is attained by looking at multiple nodes of the branch-and-bound search tree simultaneously ... near-linear speedups on up to 128 processors''

MINTO, Mixed INTeger Optimizer for mixed integer LPs

IBM Optimization Subroutine Library (OSL) (with a branch-and-bound mixed integer QP solver)

NAG FortMP (branch-and-bound mixed integer LP solver)

XPRESS-MP (mixed integer LP, QP and MINLP solver)

TOMLAB modeling and optimization environment. It includes, apart from many local algorithms, improved versions of the global optimization algorithms DIRECT and EGO of Jones, rbfSolve of Gutmann and Powell, Pinter's LGO, and mixed integer nonlinear solvers of Leyffer and Fletcher.

OptQuest (Tabu and Scatter search, etc.)

OptiREX, Cutting optimizer for rectangular sheets

ILOG Solver C++ software library which solves industrial problems for which generating or optimizing a solution is a highly combinatorial task, using constraint satisfaction techniques

Koalog Constraint Solver in Java

HEURO, Integrated Optimization Environment (for large scale black box global optimization with expensive objective function)

LGO Global Solver Engine for Microsoft Excel

LGO, Lipschitz global optimization, an integrated development environment for global optimization problems with Lipschitz continuous objective and constraints (by Janos Pinter)

MathOptimizer for Mathematica
constrained local and global optimization

IOSO, Indirect Optimization Based on Self-Organization in Fortran 77, for large-scale and possibly multiobjective inequality constrained problems
heuristic: builds local statistical models from function values and optimizes these

Constrained Global Optimization with Mathematica (including mixed integer problems and 0-1 integer problems) using adaptive grid refinement (by Loehle Enterprises, commercial)

Generator, Genetic Algorithm (for Excel worksheets)
``You can use Generator to maximize profits...'' (... of New Light Industries, Ltd., of course)

Magestic, Data Fitting by Global Optimization (for Excel worksheets, commercial)

GLO Global Local Optimizer (by Michael J. Murphy)
genetic algorithm for expensive black box (finite element) objective functions with constraints

Pointer, Constrained Optimization Tool with automatic selection or combination of up to four different search algorithms, including their tuning parameters (by Synaps, Inc.)

``Options for global optimization include algorithms based on cluster analysis and Monte Carlo techniques.''

Curvi for bound constrained optimization (by Windward Technologies)

OPTECH guided stochastic search for constrained global optimization

GEATbx Matlab Genetic and Evolutionary Algorithm Toolbox (by Hartmut Pohlheim)

Astrokettle Bin Packing in 2D and 3D

HIRON, stochastic global search for multivariate functions on a box

GIRAFFE Production Scheduling

UNICALC Interval Branch and Bound (by Alexander Semenov)
accepts inequality and/or equality constraints and decision variables (free demo version)

CLP(BNR), Constraint Logic Programming for Boolean, Natural and Real variables

ECLiPSe, ECRC Constraint Logic Parallel System constraint satisfaction (cheap for academic users)

IF/Prolog Prolog constraint satisfaction package

CHIP Prolog, C, and C++ programs for constraint satisfaction and scheduling

Constraint Logic Programming over Finite Domains in SICStus Prolog

Integer Programming Links from the Optimization Software Guide

Some of My Other Pages

Global (and Local) Optimization

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Statistics Links
Computational Mathematics Links
Mathematical Software

Interval Methods
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