Overview of Optimization Software: Free, Open‑Source, and Proprietary Solutions

Given a function f: A \to \mathbb{R} , the goal of an optimization problem is to find an element x_0 \in A such that f(x_0) \le f(x) for all x \in A . In continuous optimization, A is a subset of Euclidean space \(\mathbb{R}^n\) defined by constraints, while in combinatorial optimization A is a discrete set such as binary strings, permutations, or integer sets.

Optimization software requires the objective function f to be implemented in a suitable programming language and linked at compile‑time or run‑time. The software evaluates f(x) for candidate inputs from A and may also request derivative information, enabling modular testing of different functions with the same optimizer.

The following tables list notable optimization packages organized by license and business model.

Free and Open‑Source Software

Applications (illustrated by images in the original source)

Software libraries (illustrated by images in the original source)

Proprietary Software

AIMMS – goal‑oriented modeling system with GUI support

ALGLIB – dual‑licensed C++/C# library for quadratic and nonlinear optimization

Altair HyperStudy – experimental design and multidisciplinary optimization

AMPL – modeling language for large‑scale linear, mixed‑integer, and nonlinear problems

ANTIGONE – deterministic global MINLP solver

APMonitor – modeling language and suite for large‑scale nonlinear, mixed‑integer, differential and algebraic equations (MATLAB, Python, Julia interfaces)

Artelys Knitro – large‑scale nonlinear optimization for continuous and mixed‑integer problems

ASTOS – aerospace ballistic optimization software

BARON – global optimization for algebraic nonlinear and mixed‑integer problems

COMSOL Multiphysics – cross‑platform finite‑element analysis and multiphysics simulation

CPLEX – integer, linear, and quadratic programming

FEATool Multiphysics – MATLAB GUI toolbox for multiphysics FEA

FICO Xpress – integer, linear, quadratic, and nonlinear programming

FortMP – integer, linear, and quadratic programming

FortSP – stochastic programming

HEEDS MDO – multidisciplinary design optimization with adaptive algorithms

IMSL Numerical Libraries – optimization algorithms for C, Java, C#, .NET, Fortran, Python

IOSO – self‑organizing indirect optimization for multi‑objective nonlinear problems

Kimeme – open platform for multi‑objective and multidisciplinary design optimization

LINDO – linear, integer, nonlinear, stochastic, and global optimization suite

LIONsolver – integrated software for data mining, modeling, and intelligent optimization

modeFRONTIER – platform for multi‑objective, multidisciplinary optimization with engineering tool integration

Maple – linear, quadratic, nonlinear, continuous, and integer optimization with global options

MATLAB Optimization Toolbox – linear, integer, quadratic, nonlinear, multi‑objective, nonsmooth problems and parameter estimation

MIDACO – evolutionary‑based single‑ and multi‑objective optimizer with many language gateways

Mathematica – large‑scale constrained/unconstrained linear and nonlinear continuous and integer optimization

ModelCenter – graphical environment for integrated design optimization

MOSEK – linear, quadratic, conic, and convex nonlinear continuous and integer optimization

NAG – extensive collection of linear, quadratic, nonlinear, sparse, and global optimization routines

NMath – linear, quadratic, and nonlinear programming

OptimJ – Java‑based modeling language with support for GLPK, CPLEX, etc.

Optimus – Noesis Solutions workflow integration and optimization platform

optiSLang – CAE‑based sensitivity, optimization, and robustness assessment

OptiY – modern optimization environment for uncertainty, reliability, and data mining

OptiStruct – award‑winning CAE technology for conceptual and structural optimization

PottersWheel – ODE parameter estimation (MATLAB toolbox, free for academia)

pSeven – engineering simulation automation and multidisciplinary optimization platform

SAS – analytics suite covering statistics, forecasting, machine learning, and optimization

SmartDO – global multidisciplinary design optimization for CAE

SNOPT – large‑scale optimization solver

The Unscrambler X – product formulation and process optimization

TOMLAB – MATLAB‑based global, integer, least‑squares, linear, quadratic, and unconstrained optimization (supports Gurobi, CPLEX, SNOPT, KNITRO, MIDACO)

VisSim – visual block‑diagram language for dynamic system simulation and optimization

WORHP – large‑scale sparse continuous nonlinear optimizer

Freeware / Free for Academic Use

AIMMS

AMPL

APMonitor – free for both academic and commercial use, integrates with Julia, Python, MATLAB

ASTOS

CPLEX

Couenne – open‑source deterministic global MINLP solver (Eclipse Public License)

FICO Xpress

Galahad library

GEKKO Python

Gurobi

LIONsolver

MIDACO – evolutionary computation based numerical optimizer

MINTO – branch‑and‑bound integer programming solver (free for personal use)

MOSEK – large‑scale optimizer for linear, quadratic, conic, convex nonlinear, continuous, and integer problems

OptimJ – Java modeling language (free version supports lp_solve, GLPK, LP/MPS formats)

PottersWheel – ODE parameter estimation (free MATLAB toolbox for academia)

SCIP – free for non‑commercial and academic research

WORHP

Additional References

Optimization software comparisons

Computer algebra system lists

Constraint programming language lists

Numerical library overviews

Optimization algorithm lists

SMT solver lists

For further discussion, join the community channels listed in the original source (WeChat public account, QQ group, knowledge circles, etc.).