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List of optimization software

From Wikipedia, the free encyclopedia

Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process. Many real-world problems can be modeled in this way. For example, the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs can be business choices and the output can be the obtained profit.

An optimization problem, (in this case a minimisation problem), can be represented in the following way:

Given: a function f : A R from some set A to the real numbers
Search for: an element x0 in A such that f(x0) ≤ f(x) for all x in A.

In continuous optimization, A is some subset of the Euclidean space Rn, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers.

The use of optimisation software requires that the function f is defined in a suitable programming language and connected at compile or run time to the optimisation software. The optimisation software will deliver input values in A, the software module realizing f will deliver the computed value f(x) and, in some cases, additional information about the function like derivatives.

In this manner, a clear separation of concerns is obtained: different optimisation software modules can be easily tested on the same function f, or a given optimisation software can be used for different functions f.

The following tables provide a list of notable optimisation software organised according to license and business model type.

Free and open-source software[edit]


Name License Description
ADMB BSD nonlinear optimization framework, using automatic differentiation.
ASCEND GPL mathematical modelling chemical process modelling system.
CUTEr GPL testing environment for optimization and linear algebra solvers.
GNU Octave GPL software package featuring a high-level programming language, primarily intended for numerical computations; well recognized free alternative to MATLAB.
Octeract Engine Community Octeract EULA parallel deterministic global MINLP solver. Octeract Engine Community is a full version of the solver that is free to use for any purpose.
Scilab CeCILL cross-platform numerical computational package and a high-level, numerically oriented programming language with free numerical optimization framework.

Software libraries[edit]

Name License Description
ALGLIB GPL dual licensed (GPL/commercial) optimization library (LP, QP and nonlinear programming problems), optionally using automatic differentiation. Cross-language: C++, C#.
COIN-OR EPL 1.0 integer programming, linear programming, nonlinear programming.
Dlib BSL‑1.0 unconstrained/box-constrained nonlinear/QP optimization library written in C++.
GEKKO MIT machine learning and optimization of mixed-integer and differential algebraic equations in Python.
GLPK GPL GNU Linear Programming Kit with C API.
HiGHS MIT linear programming (LP), mixed integer programming (MIP), and convex quadratic programming (QP).[1]
IPOPT EPL (was CPL) large scale nonlinear optimizer for continuous systems (requires gradient), C++ (formerly Fortran and C). It became a part of COIN-OR.[2]
MINUIT (now MINUIT2) LGPL unconstrained optimizer internally developed at CERN.
OpenMDAO Apache License Multidisciplinary Design, Analysis, and Optimization (MDAO) framework, written in Python. The development is led out of the NASA Glenn Research Center, with support from the NASA Langley Research Center.
OptaPlanner Apache License Java constraint solver with construction heuristics and metaheuristics. Integrates with Spring Boot and Quarkus. Runs on Kotlin and Scala too.
SCIP Apache License solver for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP).
SciPy BSD general numeric package for Python, with some support for optimization.

Proprietary software[edit]

  • AIMMS – optimisation modelling system, including GUI building facilities.
  • ALGLIB – dual licensed (GPL/commercial) constrained quadratic and nonlinear optimisation library with C++ and C# interfaces.
  • Altair HyperStudy – design of experiments and multidisciplinary design optimisation.
  • AMPL – modelling language for large-scale linear, mixed integer and nonlinear optimisation.
  • ANTIGONE – a deterministic global optimization MINLP solver.
  • APMonitor – modelling language and optimisation suite for large-scale, nonlinear, mixed integer, differential and algebraic equations with interfaces to MATLAB, Python, and Julia.
  • Artelys Knitro – large scale nonlinear optimisation for continuous and mixed-integer programming.
  • ASTOS – AeroSpace Trajectory Optimisation Software for launcher, re-entry and generic aerospace problems.
  • BARON – optimisation of algebraic nonlinear and mixed-integer nonlinear problems.
  • COMSOL Multiphysics – a cross-platform finite element analysis, solver and multiphysics simulation software.
  • CPLEX – solver for linear and quadratic programming with continuous or integer variables (MIP).
  • FEATool Multiphysics – FEA GUI Toolbox for MATLAB.
  • FICO Xpress – solver for linear and quadratic programming with continuous or integer variables (MIP).
  • FortMP – linear and quadratic programming.
  • FortSP – stochastic programming.
  • GAMS – General Algebraic Modeling System.
  • Gurobi Optimizer – solver for linear and quadratic programming with continuous or integer variables (MIP).
  • HEEDS MDO – multidisciplinary design optimisation using SHERPA, a hybrid, adaptive optimisation algorithm.
  • IMSL Numerical Libraries – linear, quadratic, nonlinear, and sparse QP and LP optimisation algorithms implemented in standard programming languages C, Java, C# .NET, Fortran, and Python.
  • IOSO – (Indirect Optimisation on the basis of Self-Organisation) a multi-objective, multidimensional nonlinear optimisation technology.
  • Kimeme – an open platform for multi-objective optimisation and multidisciplinary design optimisation.
  • LINDO – (Linear, Interactive, and Discrete Optimiser) a software package for linear programming, integer programming, nonlinear programming, stochastic programming, and global optimisation. The "What's Best!" Excel add-in performs linear, integer, and nonlinear optimization using LINDO.
  • LIONsolver – an integrated software for data mining, analytics, modelling Learning and Intelligent OptimizatioN and reactive business intelligence approach.
  • modeFRONTIER – an integration platform for multi-objective and multidisciplinary optimization, which provides a seamless coupling with third party engineering tools, enables the automation of the design simulation process, and facilitates analytic decision-making.
  • Maple – linear, quadratic, and nonlinear, continuous and integer optimisation. Constrained and unconstrained. Global optimization with add-on toolbox.
  • MATLAB – linear, integer, quadratic, and nonlinear problems with Optimization Toolbox; multiple maxima, multiple minima, and non-smooth optimisation problems; estimation and optimisation of model parameters.
  • MIDACO a lightweight software tool for single- and multi-objective optimization based on evolutionary computing. Written in C/C++ and Fortran with gateways to Excel, VBA, Java, Python, Matlab, Octave, R, C# and Julia.
  • Mathematica – large-scale multivariate constrained and unconstrained, linear, quadratic and nonlinear, continuous and integer optimisation.
  • ModelCenter – a graphical environment for integration, automation, and design optimisation.
  • MOSEK – linear, quadratic, conic and convex nonlinear, continuous and integer optimisation.
  • NAG – linear, quadratic, nonlinear, sums of squares of linear or nonlinear functions; linear, sparse linear, nonlinear, bounded or no constraints; local and global optimisations; continuous or integer problems.
  • NMath – linear, quadratic and nonlinear programming.
  • Octeract Engine – a deterministic global optimization MINLP solver. Octeract Engine Community is free to use, and paid plans exist for additional features.
  • OptimJ – Java-based modelling language. Premium Edition includes support for Mosek and CPLEX solvers.
  • Optimus platform – a process integration and design optimisation platform developed by Noesis Solutions.
  • optiSLang – software solutions for CAE-based sensitivity analysis, optimisation and robustness evaluation.
  • OptiY – a design environment providing modern optimisation strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta modelling.
  • OptiStruct – award-winning CAE technology for conceptual design synthesis and structural optimisation.
  • PottersWheel – parameter estimation in ordinary differential equations (MATLAB toolbox, free for academic use).
  • pSeven – software platform for automation of engineering simulation and analysis, multidisciplinary optimisation and data mining, developed by DATADVANCE.
  • SAS – a software suite developed by SAS Institute for advanced analytics (statistics, forecasting, machine learning, optimisation, etc.), business intelligence, customer intelligence, data management, risk management, and many more.
  • SmartDO – multidisciplinary global design optimisation, specialised in computer-aided engineering (CAE). using the direct global search approaches.
  • SNOPT – large-scale optimisation problems.
  • The Unscrambler – product formulation and process optimisation software.
  • TOMLAB – supports global optimisation, integer programming, all types of least squares, linear, quadratic and unconstrained programming for MATLAB. TOMLAB supports solvers like CPLEX, SNOPT, KNITRO and MIDACO.
  • VisSim – a visual block diagram language for simulation and optimisation of dynamical systems.
  • WORHP – a large-scale sparse solver for continuous nonlinear optimisation.

Freeware/free for academic use[edit]

See also[edit]


  1. ^ Hall, Julian (21 September 2020). HiGHS: High-performance open-source software for linear optimization (PDF). Edinburgh, United Kingdom: University of Edinburgh. Retrieved 2022-02-27. Presentation.
  2. ^ "Projects". COIN-OR: Computational Infrastructure for Operations Research. 8 October 2014. Retrieved 10 March 2021.