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List of optimization software
List of optimization software
List of optimization software
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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 could be design parameters for a motor, the output could be the power consumption. For another optimization, the inputs could be business choices and the output could be the profit obtained.

An optimization problem, (in this case a minimization 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 optimization software requires that the function f is defined in a suitable programming language and connected at compilation or run time to the optimization software. The optimization 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 optimization software modules can be easily tested on the same function f, or a given optimization software can be used for different functions f.

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

Free and open-source software

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Applications

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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 using a high-level programming language, primarily intended for numerical computations; it is mostly compatible with MATLAB.
Scilab CeCILL cross-platform numerical computational package and a high-level, numerically oriented programming language with a numerical optimization framework.

Software libraries

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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.
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

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  • AIMMS – optimization modelling system, including GUI building facilities.
  • ALGLIB – dual licensed (GPL/commercial) constrained quadratic and nonlinear optimization library with C++ and C# interfaces.
  • Altair HyperStudy – design of experiments and multidisciplinary design optimization.
  • AMPL – modelling language for large-scale linear, mixed integer and nonlinear optimization.
  • ANTIGONE – a deterministic global optimization MINLP solver.
  • APMonitor – modelling language and optimization suite for large-scale, nonlinear, mixed integer, differential, and algebraic equations with interfaces to MATLAB, Python, and Julia.
  • Artelys Knitro – large scale nonlinear optimization for continuous and mixed-integer programming.
  • ASTOS – AeroSpace Trajectory optimization Software for launch, re-entry, and generic aerospace problems.
  • BARON – optimization 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 optimization using SHERPA, a hybrid, adaptive optimization algorithm.
  • IMSL Numerical Libraries – linear, quadratic, nonlinear, and sparse QP and LP optimization algorithms implemented in standard programming languages C, Java, C# .NET, Fortran, and Python.
  • IOSO – (Indirect optimization on the basis of Self-Organization) a multi-objective, multidimensional nonlinear optimization technology.
  • Kimeme – an open platform for multi-objective optimization and multidisciplinary design optimization.
  • LINDO – (Linear, Interactive, and Discrete optimizer) a software package for linear programming, integer programming, nonlinear programming, stochastic programming, and global optimization. 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 optimization. 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 optimization problems; estimation and optimization 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 optimization.
  • ModelCenter – a graphical environment for integration, automation, and design optimization.
  • MOSEK – linear, quadratic, conic and convex nonlinear, continuous, and integer optimization.
  • NAG – linear, quadratic, nonlinear, sums of squares of linear or nonlinear functions; linear, sparse linear, nonlinear, bounded or no constraints; local and global optimizations; continuous or integer problems.
  • NMath – linear, quadratic and nonlinear programming.
  • Octeract Engine – a deterministic global optimization MINLP solver. 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 optimization platform developed by Noesis Solutions.
  • optiSLang – software solutions for CAE-based sensitivity analysis, optimization, and robustness evaluation.
  • OptiY – a design environment providing modern optimization 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 optimization.
  • OptQuest – metaheuristics-based optimization plugin for simulation-based optimization in conjunction with discrete-event simulation software.
  • PottersWheel – parameter estimation in ordinary differential equations (MATLAB toolbox, free for academic use).
  • pSeven – software platform for automation of engineering simulation and analysis, multidisciplinary optimization and data mining, developed by DATADVANCE.
  • SAS – a software suite developed by SAS Institute for advanced analytics (statistics, forecasting, machine learning, optimization, etc.), business intelligence, customer intelligence, data management, risk management, and many more.
  • SmartDO – multidisciplinary global design optimization, specialized in computer-aided engineering (CAE). using the direct global search approaches.
  • SNOPT – large-scale optimization problems.
  • The Unscrambler – product formulation and process optimization software.
  • TOMLAB – supports global optimization, 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 optimization of dynamical systems.
  • WORHP – a large-scale sparse solver for continuous nonlinear optimization.

Freeware/free for academic use

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See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

List of optimization software

View on Grokipedia
from Grokipedia
A list of optimization software compiles computational tools and libraries engineered to solve mathematical optimization problems, which entail identifying variable values that minimize or maximize an objective function while adhering to specified constraints, such as equality, inequality, or integrality conditions. These programs implement specialized algorithms to handle diverse problem classes, including (LP), where all relations are linear; (NLP), involving continuous nonlinear objectives; and mixed-integer programming (MIP), incorporating discrete variables. Optimization software underpins decision-making across sectors like , design, , , and energy systems, enabling efficient resource allocation and complex system analysis. Prominent examples include commercial solvers such as Gurobi for LP, MILP, (QP), and MIQP; CPLEX for similar broad-spectrum optimization; and Knitro for large-scale NLP challenges. Open-source alternatives encompass SCIP Optimization Suite for constraint integer programming and , for large-scale NLP, and GLPK for LP and MIP. This catalog categorizes entries by problem type and solver capabilities, reflecting ongoing advancements in performance, scalability, and integration with and quantum techniques as of 2025.

Open-source software

Standalone applications

Standalone open-source optimization software encompasses complete applications designed for end-users to formulate, solve, and analyze optimization problems directly, often through command-line interfaces, scripting, or integrated development environments, without requiring embedding into larger codebases. These tools span domains such as statistical modeling, , and numerical solving, supporting a range of problem types from nonlinear to mixed-integer programming. They emphasize accessibility, extensibility, and community-driven development, enabling researchers and practitioners to tackle complex optimizations efficiently. ADMB is an automatic differentiation-based tool for nonlinear optimization and statistical modeling, primarily used for maximum likelihood estimation in complex statistical models such as those in fisheries and resource management. Developed by David Fournier at Otter Research Ltd. starting in the late 1980s, it gained prominence in the 1990s for its applications in nonlinear problems and became open-source in 2007 under the management of the ADMB Foundation, supported by organizations like NOAA Fisheries and the Gordon and Betty Moore Foundation. Key features include reverse-mode automatic differentiation via the C++ AUTODIF library for efficient gradient computation, numerical stability in model fitting, and support for random effects models through ADMB-RE, all released under a BSD-like license. ASCEND serves as a modeling environment for equation-based simulation and optimization, particularly in chemical , allowing users to define models declaratively and solve them using integrated solvers. Originating from research at in the 1980s, it evolved into an open-source project under the GNU General Public License (GPL), with updates such as Mac OS X compatibility in version 0.9.7 released in 2009 and further enhancements in version 0.9.8, including GitHub integration, as of 2024. Core capabilities include object-oriented equation modeling for steady-state and dynamic systems, , and seamless integration with external solvers like for nonlinear optimization, providing exact second derivatives to enhance convergence. CUTEr, now evolved into CUTEst, provides a comprehensive collection of over 1,000 test problems for optimization algorithms, covering constrained and unconstrained nonlinear, linear, and quadratic formulations in a standardized format. Released under the GNU Lesser General Public License (LGPL) version 3.0, it originated as a versatile testing environment in the 1990s and received major updates in the 2000s, with modern enhancements like thread-safe 77/90 code and dynamic memory allocation introduced in versions such as 2.3.0 (2013) and 2.5.1 for support. Its primary role is in algorithm validation and comparison, facilitating reproducible experiments across platforms without altering problem data. is a high-level interpreted for numerical computations, featuring optimization solvers through core functions and the optional 'optim' package, which enables solving nonlinear least-squares problems and other optimization tasks through functions like lsqnonlin. Licensed under the GNU General Public License (GPL), it maintains high compatibility with syntax and toolboxes, allowing users to port scripts with minimal changes for tasks like unconstrained and . Developed as a free alternative since the , its latest stable release (version 10.3.0 in 2025) supports cross-platform execution on , macOS, and Windows, with visualization tools for result analysis. Scilab functions as an open-source platform for numerical computation and scientific visualization, incorporating optimization functions for solving various differentiable and non-differentiable problems, including nonlinear via optim, quadratic via quapro, least-squares via lsqrsolve, and semi-definite programming through add-on modules. Distributed under the CeCILL license (compatible with GPL), it integrates the Xcos graphical editor for modeling and simulating hybrid dynamic systems, facilitating dynamic optimization by combining block diagrams with optimization routines for control and applications. This setup supports equation-based workflows similar to /, with hundreds of built-in functions for multidisciplinary engineering tasks. HiGHS is a high-performance standalone solver for (LP), mixed-integer programming (MIP), and convex quadratic programming (QP), capable of handling large-scale sparse models through a command-line . Licensed under the since its initial release in 2020, it leverages for serial and , including multi-threaded simplex and interior-point methods to accelerate solves on modern hardware. Benchmarks demonstrate it outperforming certain commercial solvers in speed and scalability for MIP instances, as evidenced in comparative tests on standard problem sets. These applications can extend functionality by integrating with libraries like for advanced scripting in Python environments.

Libraries and frameworks

is a cross-platform and library that includes optimization routines for solving linear, nonlinear, and least-squares problems. It provides bindings for C++, C#, , and Python, enabling seamless integration into diverse applications, and supports multicore processing for enhanced performance on modern hardware. The free edition is distributed under the GNU General Public License version 2 or later. COIN-OR (Computational Infrastructure for ) is an open-source initiative launched in 2000 with initial funding from the U.S. Department of Energy, comprising a collection of interoperable tools for . Key components include CBC, a branch-and-cut solver for mixed-integer programming, and Clp, an implementation of the for . All software in the project is released under the version 2.0. Dlib is a modern C++ toolkit that incorporates algorithms alongside optimization solvers, such as the L-BFGS method for large-scale unconstrained problems. It is particularly utilized in tasks, including face recognition, where optimization supports feature extraction and model training. The library is licensed under the Boost Software License 1.0. GEKKO is a Python package tailored for nonlinear optimization and dynamic simulation of differential algebraic equations, featuring an equation-oriented modeling approach that parses symbolic expressions for solver input. It finds applications in (APC), where it optimizes industrial processes like chemical reactors and energy systems. GEKKO is distributed under the . GLPK (GNU Linear Programming Kit) provides solvers for large-scale (LP) and mixed-integer programming (MIP) problems, employing the and primal-dual interior-point algorithms. It offers a callable API with bindings available for Python via the GLPKMathProg package and for through the Rglpk interface. The package is licensed under the GNU General Public License version 3. IPOPT (Interior Point Optimizer) is designed for large-scale , utilizing primal-dual barrier methods with options for limited-memory quasi-Newton approximations of the Hessian to handle sparse problems efficiently. It integrates directly with modeling languages like AMPL and frameworks such as Pyomo for defining and solving optimization models. is released under the . MINUIT is a minimization package developed at for fitting parameters in multi-parameter functions, commonly applied in for likelihood maximization and error analysis through methods like the MIGRAD algorithm. It supports both and C++ implementations, with the latter integrated into the framework for object-oriented use. MINUIT is licensed under the GNU Lesser General Public License version 2.1. OpenMDAO is a multidisciplinary and optimization (MDAO) framework that facilitates the modeling of coupled systems through component-based workflows and supports drivers like SLSQP for sequential quadratic programming-based optimization. It enables efficient handling of complex, derivative-enabled simulations in fields such as . The framework is distributed under the version 2.0. SCIP (Solving Constraint Integer Programs) serves as a framework for constraint integer programming, incorporating branch-and-cut-and-price techniques for mixed-integer linear and nonlinear problems, with extensible plugins for handling nonlinear constraints via convex relaxations. It allows developers to customize the solving process through modular constraint handlers and separators. SCIP has been licensed under the version 2.0 since version 8.0.3 in the . SciPy's optimize module offers a suite of algorithms for unconstrained and constrained optimization, including quasi-Newton methods like BFGS for smooth functions, derivative-free approaches such as COBYLA for nonlinear constraints, and trust-region methods for robust convergence. It provides a unified minimize interface for multivariate scalar functions, making it accessible for scientific computing workflows. SciPy is released under the BSD License.

Proprietary and commercial software

General-purpose solvers

General-purpose solvers encompass proprietary software packages that address a wide array of problems, including (LP), (QP), (NLP), mixed-integer programming (MIP), and mixed-integer quadratic programming (MIQP), using advanced algorithms suitable for diverse applications in , , and . These tools often integrate modeling languages, graphical user interfaces (GUIs), and solver engines, enabling users to formulate, solve, and analyze complex models efficiently. Unlike domain-specific software, they prioritize versatility and scalability for general mathematical formulations. AIMMS is a commercial modeling system introduced in the 1990s, featuring an algebraic modeling language and seamless integration with external solvers for building and deploying optimization applications. It provides a GUI for intuitive model development, scenario analysis, and visualization, with native support for MIP through interfaces to solvers like CPLEX and Gurobi, facilitating rapid prototyping and cloud-based deployment. AMPL is a proprietary algebraic modeling language developed at Bell Labs in 1988, offering an integrated development environment (IDE) for formulating large-scale optimization problems in a concise, mathematical syntax. It connects to over 100 solvers for LP, NLP, MIP, and other problem classes, supporting scripting, debugging, and deployment across platforms, which streamlines the transition from model specification to solution. BARON is a commercial global optimization solver specializing in nonlinear and mixed-integer nonlinear programming (MINLP), employing branch-and-reduce algorithms to systematically explore the solution space and guarantee global optimality for nonconvex problems. It handles continuous, integer, and mixed-integer formulations efficiently, with recent versions enhancing performance for industrial-scale MINLPs through presolving and relaxation techniques. CPLEX, developed by since the , is a optimizer for LP, QP, MIP, and MIQP, utilizing dual , barrier, and sifting algorithms alongside parallel processing for high-speed solutions on large models. It includes extensive tuning parameters for customizing solver behavior, such as presolve levels and branching strategies, making it suitable for and scheduling tasks. GAMS (General Algebraic Modeling System) is a proprietary high-level modeling platform for LP, NLP, and MIP, emphasizing database integration for data import/export and built-in tools for scenario , particularly in and economic modeling. It compiles models into solver-compatible formats and supports multi-solver execution, enabling comparative studies and what-if analyses on complex systems. Gurobi Optimizer is a high-performance proprietary solver for LP, MIP, QP, and related problems, offering free academic licenses while providing commercial scalability through deployment and machine learning-based tuning in updates from the 2020s. It leverages multicore parallelism and advanced heuristics for rapid convergence on million-variable models, with APIs in multiple languages for integration. LINDO is a proprietary optimization suite for linear, nonlinear, and , incorporating the and a global solver for NLP alongside extensions for and multi-objective problems. It features an intuitive interface for model building and supports branch-and-bound for integer solutions, with tools for and in uncertain environments. MOSEK is a proprietary solver for conic, LP, QP, and (SDP), relying on interior-point methods for high-precision solutions to convex problems with sparse structures. It provides and Python APIs for embedding in applications, along with support for mixed-integer conic optimization via branch-and-bound, optimized for financial and engineering formulations. SNOPT is a proprietary sparse nonlinear optimizer designed for large-scale NLP and nonlinearly constrained problems, implementing (SQP) with feasibility restoration phases to handle ill-posed constraints effectively. It exploits sparsity in Jacobians and Hessians for computational efficiency, making it ideal for aerodynamic design and applications. TOMLAB is a MATLAB-based optimization environment that integrates base solvers for LP, QP, NLP, and MIP, with add-ons for robust and to address uncertainty in parameters. It offers a unified interface for modeling, solving, and post-processing, including global search capabilities and parameter estimation tools for applied engineering problems. For users seeking cost-effective alternatives, open-source solvers like GLPK provide similar capabilities for LP and basic MIP without licensing fees.

Domain-specific tools

Domain-specific tools encompass proprietary software packages engineered for optimization challenges within targeted industries, such as engineering design, , , , , and . These tools integrate domain-tailored algorithms, interfaces, and automations to address practical constraints like multiphysics interactions, large-scale decision modeling, and black-box processes, often embedding general-purpose solvers like CPLEX as computational backends for enhanced scalability. Unlike broad mathematical solvers, they prioritize industry-specific integrations and user-friendly environments for rapid deployment in real-world applications. Altair HyperStudy, developed by , is a proprietary multidisciplinary platform for (CAE) applications. It supports (DOE) to systematically vary input parameters, approximation modeling via response surfaces and for predictive design exploration, and tight integration with HyperMesh for preprocessing and simulation workflows, with capabilities established since the early 2000s. Artelys Knitro, from Artelys, serves as a nonlinear solver optimized for enterprise-scale problems in and sectors. It employs active-set (SQP) and interior-point barrier methods to handle large-scale (NLP) tasks, including and optimal power flow, with support for mixed-integer NLP (MINLP) extensions. COMSOL Multiphysics Optimization Module, an add-on to the COMSOL Multiphysics platform by COMSOL AB, facilitates optimization of PDE-constrained problems across coupled physics domains like electromagnetics, , and . It incorporates multiphysics coupling for holistic simulations and to compute gradients efficiently, enabling parameter, shape, and optimizations with gradient-based solvers such as MMA and . FICO Xpress, provided by , is a proprietary optimization suite for decision management in banking and retail industries. It features the for declarative problem formulation and distributed mixed-integer programming (MIP) solving to tackle large-scale linear, quadratic, and nonlinear models, supporting applications like assessment and inventory allocation. FortMP, from Maximal Software, functions as a proprietary parallel solver for large-scale (LP) and mixed-integer programming (MIP) in and operational . It utilizes sparse simplex methods with primal and dual variants, alongside interior-point methods, and scales via parallel processing for MIP, making it suitable for routing and . LIONsolver, part of the LION (Learning and Intelligent Optimization) framework by the LION Association, is a tool for intelligent optimization of black-box problems in and . It incorporates nature-inspired algorithms such as within reactive search optimization, enabling self-tuning parameters and data-driven digital twins for noisy, ill-defined systems like process tuning and . MATLAB Optimization Toolbox, offered by as a extension to , provides a suite of algorithms for optimization in engineering design and development. It includes genetic algorithms for global search in multimodal landscapes and pattern search for of nonlinear problems, supporting constrained parameter estimation and multiobjective trade-offs. modeFRONTIER, developed by ESTECO, is a platform for process integration and in automotive and . It automates workflows by linking CAD/CAE tools and solvers, generating multi-objective Pareto fronts through DOE, response surface modeling, and AI-driven exploration to balance objectives like weight reduction and performance enhancement. NAG Library, from the Numerical Algorithms Group (NAG), is a numerical software collection with dedicated optimization routines for finance and risk management applications. It offers Fortran and C APIs for accessing solvers in linear, nonlinear, and , including scenario-based methods for and uncertainty handling. SAS Optimization, integrated within the proprietary SAS suite by , targets and marketing optimization challenges. It embeds genetic algorithms for evolutionary search and heuristic solvers for nonlinear, nonconvex problems, facilitating parallel processing and techniques like Dantzig-Wolfe for large-scale network flows in and customer segmentation.

Freeware and academic licenses

Free for non-commercial use

Software in this category is distributed freely for non-commercial, , or personal applications, often with licensing that permits such use while restricting commercial deployment due to dependencies on academic-licensed components or explicit terms. These tools provide valuable capabilities for optimization tasks in and exploratory settings, researchers to tackle complex problems without incurring costs, though users must transition to fully licensed alternatives for production environments. Bonmin is an open-source solver developed within the initiative for mixed-integer (MINLP) problems, employing a branch-and-bound framework to minimize objective functions subject to nonlinear constraints and integer requirements. It incorporates hybrid algorithms such as the B-Hyb method, which combines interior-point optimization via with outer-approximation decomposition, originating from developments in the early 2000s to handle convex MINLPs efficiently. While the core Bonmin code is licensed under the (EPL) for broad use, its recommended sparse linear solver, MA27 from the Harwell Subroutine Library (HSL), is available only for non-commercial purposes; however, commercial use is possible with open-source alternatives like WSMP. Couenne extends capabilities for non-convex MINLP problems through a branch-and-bound approach that generates convex over- and under-estimators of nonlinear functions to compute tight relaxations and lower bounds. Released under the EPL as part of , it employs spatial branching techniques to refine search spaces and achieve global optima, making it suitable for deterministic verification in research applications. Like Bonmin, Couenne relies on underlying solvers such as for nonlinear subproblems; while some linear algebra components like MA27 impose non-commercial restrictions, commercial use is feasible with open-source dependencies. The community edition of serves as a premier interior-point solver for large-scale (NLP) problems, optimizing twice-continuously differentiable objectives with bound and equality constraints using a filter line-search method. Distributed under the EPL via , this version is fully functional for both non-commercial and commercial NLP solving but may require selection of appropriate linear solvers; open options like (LGPL) permit commercial use, while HSL components (including MA27) are limited to non-commercial settings.

Academic editions of commercial software

Academic editions of commercial optimization software provide students, educators, and researchers with free or discounted access to full-featured solvers, typically under verified academic licenses that restrict use to non-commercial purposes such as , coursework, and . These programs often include renewable licenses, integration resources, and support tailored for educational environments, enabling hands-on learning of advanced optimization techniques without the barriers of commercial pricing. Eligibility usually requires affiliation with accredited institutions, verified through academic email addresses or institutional details, and licenses may transition to paid versions upon entering commercial roles. The ILOG CPLEX Optimization Studio Academic Initiative offers the complete version of CPLEX at no cost to faculty, research professionals, and students at accredited institutions. Expanded in 2020 to explicitly include students alongside educators, the program provides unlimited problem size capabilities and access to teaching resources such as tutorials and forums for optimization modeling. Users must register via the IBM Academic Initiative portal using institutional credentials to obtain the . Gurobi Optimization provides a no-cost, full-featured academic license for its , renewable annually for use in teaching, research, and coursework at degree-granting institutions. Eligibility is verified through a .edu or connection to an institutional network, supporting options like named-user licenses for personal machines, web-based licenses for cloud environments, and site licenses for group deployments. Integration guides, quick-start tutorials, and code examples are available to facilitate embedding Gurobi into academic workflows, such as Python or applications. MOSEK offers free academic licenses for its solver, including personal licenses for individual faculty, students, or staff and institutional floating licenses for departments or groups. These licenses, valid for 365 days (personal) or two years (institutional) and renewable indefinitely, provide full access to all features without size restrictions for educational and purposes, with dedicated support. Updates in the have enhanced capabilities for teaching mixed-integer programming (MIP) models alongside conic problems, requested via academic email. The NEOS Server, originating from in the 1990s, delivers free access to commercial solvers like KNITRO for academic submissions over the internet. Hosted by the University of Wisconsin-Madison, it features job queuing on distributed resources and interactive result visualization, allowing users to submit optimization problems in various formats without local installation. Primarily for and , the server supports over 60 solvers, including commercial ones licensed for non-commercial use. FICO Xpress provides an academic license free to faculty and students, featuring the full Xpress Solver (including Optimizer, NonLinear, and Global variants), Mosel , for development, and for visualization, with no restrictions on problem size. Renewable annually for one year at a time, it covers linear, mixed-integer, quadratic, and nonlinear problems via APIs in Python, , , and other languages, supported by community resources. Cloud-based solving options are available through the related Community License, which academics can also access for extended modeling without solver limits on Mosel. Upon graduation or transition to industry, users of these academic editions must purchase proprietary full versions to continue commercial applications.

Specialized optimization software

Machine learning and AI optimization

Machine learning and AI optimization encompasses software tools designed to automate the tuning of hyperparameters, neural network architectures, and model configurations in machine learning workflows, leveraging techniques such as and evolutionary search to enhance performance without manual intervention. These tools integrate seamlessly with popular frameworks like and , enabling efficient exploration of complex search spaces for tasks ranging from to . Optuna is an open-source hyperparameter optimization framework released in 2018 under the , featuring a define-by-run that allows dynamic construction of search spaces during optimization. It supports efficient pruning algorithms, such as the Successive Halving Algorithm (SHA) and Median Pruning, to early-terminate unpromising trials and reduce computational waste. Optuna integrates natively with deep learning libraries including and through its integration package, facilitating distributed optimization across multiple workers. Hyperopt is a Python for serial and parallel , licensed under the BSD license and introduced in 2013. It employs the tree-structured Parzen estimator (TPE) as a core algorithm, which models the objective function using density estimates to balance exploration and exploitation in awkward search spaces. For , Hyperopt utilizes via its MongoTrials class to store and synchronize trial results across asynchronous workers, enabling scalable experimentation on clusters. Ray Tune, part of the Ray distributed computing ecosystem and released in 2019 under the Apache 2.0 license, provides scalable hyperparameter tuning with support for fault-tolerant experimentation. It incorporates the Asynchronous Successive Halving Algorithm () scheduler, which dynamically allocates resources to promising configurations by iteratively halving underperformers and promoting top candidates. Ray Tune's integration with Ray's ensures resilience to node failures, allowing seamless recovery and continuation of tuning runs in large-scale environments. Scikit-optimize (skopt) is a BSD-licensed library for tailored to pipelines, emphasizing sequential model-based approaches for expensive black-box functions. It utilizes regression as a to approximate the objective landscape, combined with acquisition functions such as expected improvement to select the next evaluation point that maximizes information gain. This setup enables efficient hyperparameter tuning for estimators, with utilities like BayesSearchCV for cross-validated searches. AutoKeras, an MIT-licensed AutoML system based on and released in 2018, automates (NAS) to discover high-performing models without requiring users to write . It employs a Bayesian optimization-guided NAS process to explore block-based architectures, supporting tasks like image classification and text regression through pre-built search spaces. AutoKeras also incorporates by fine-tuning pre-trained blocks on user data, accelerating convergence for domain-specific applications. SMAC3 is a versatile framework for sequential model-based optimization under the BSD 3-Clause license, reimplementing and extending the original SMAC tool for of algorithms. It relies on models as surrogate functions to predict performance of expensive black-box configurations, incorporating an aggressive racing mechanism to evaluate multiple incumbents in parallel. SMAC3 supports multi-fidelity evaluations and , making it suitable for tuning complex pipelines with categorical and conditional parameters. C3 AI Process Optimization is a proprietary enterprise application released as part of the C3 AI suite around 2023, designed to enhance production processes through AI-driven dynamic control recommendations. It integrates data from process historians and asset systems to build predictive optimization models using statistical and AI-based techniques, potentially incorporating mathematical methods like nonlinear programming for setpoint adjustments to improve yield and efficiency. The tool supports generative AI for rapid analysis and operates on the C3 AI Platform for scalable deployment in manufacturing environments. Timefold is an open-source optimization solver released in 2023 under the Apache 2.0 license, forked from OptaPlanner, specializing in AI-powered solutions for scheduling, routing, and planning problems. It employs constraint-solving algorithms enhanced by AI to automate large-scale operations, such as employee rostering and vehicle routing, optimizing for factors like costs, preferences, and disruptions. Timefold integrates via APIs with existing systems and supports real-time adjustments, making it suitable for operations research applications in workforce and logistics optimization. KNIME is an open-source data analytics platform under a GPL-compatible license, with extensions for AI and machine learning workflows released progressively since 2006. It enables the creation of visual workflows for process optimization using AI, including generative AI assistants for automating data science tasks like model tuning and predictive analytics. KNIME supports integration with libraries for Bayesian optimization and integrates with tools like Python and R, facilitating end-to-end optimization pipelines for business processes. DataRobot is a commercial AI platform under proprietary licensing, with version 9.0 released in March 2023, focused on automating the development and deployment of machine learning models for enterprise optimization. It streamlines workflows for hyperparameter tuning and model selection using automated techniques, supporting mathematical optimization through scalable AI infrastructure for tasks like predictive process control. The platform offers role-based tools and deployment options including cloud and on-premise, enhancing efficiency in AI-driven decision-making. H2O Driverless AI is a proprietary AutoML tool from H2O.ai, initially released in March 2018, designed to automate machine learning processes including optimization of models and features. It uses advanced algorithms for feature engineering and hyperparameter optimization, applicable to process improvement via automated black-box function evaluations and surrogate modeling. H2O Driverless AI integrates with distributed computing frameworks like Apache Spark and supports scalable experimentation for AI-enhanced optimization in various domains.

Quantum and hybrid optimization

Quantum and hybrid optimization software integrates paradigms, such as variational quantum algorithms and , with classical methods to address challenges that exceed classical computational limits. These tools typically support noisy intermediate-scale quantum (NISQ) devices and hybrid workflows, where quantum processors handle specific subproblems while classical optimizers manage overall coordination and refinement. Key examples include frameworks for implementing the Quantum Approximate Optimization Algorithm (QAOA) and (VQE), enabling applications in areas like , , and . Qiskit Optimization, an open-source module from IBM's SDK, provides tools for modeling and solving and problems directly on quantum hardware. Introduced in 2020 as part of the ecosystem, it supports high-level problem formulation with automatic conversion to quantum circuits, including QAOA for approximating solutions to NP-hard optimization tasks. The module also incorporates circuit knitting techniques to stitch together partial quantum computations for larger problems. Licensed under the Apache 2.0 license, Qiskit Optimization is available via the ecosystem repository. PennyLane is a cross-platform, open-source Python framework developed by Xanadu for differentiable , emphasizing hybrid quantum-classical workflows for optimization. It enables the implementation of hybrid VQE approaches, where quantum circuits evaluate objective functions and classical optimizers adjust parameters iteratively. The framework includes the backend for high-performance simulation of quantum circuits on classical hardware, supporting optimization tasks in and chemistry. Released under the 2.0 license, PennyLane integrates seamlessly with popular libraries for end-to-end hybrid optimization. D-Wave Ocean serves as the (SDK) for D-Wave's systems, offering open-source Python tools to formulate and solve binary quadratic optimization models. Developed since the early 2010s alongside D-Wave's hardware advancements, it features the dimod library for representing and sampling from binary quadratic models, including Ising and formulations. Ocean's hybrid solver combines with classical heuristics to tackle large-scale problems beyond the capacity of current quantum processors alone. The entire SDK is licensed under 2.0 and hosted on D-Wave's repository. Cirq, Google's open-source Python library, is designed for creating, manipulating, and optimizing quantum circuits tailored to NISQ devices, with strong support for optimization algorithms. It provides built-in noise models to simulate real-world quantum errors and parameterized gates that facilitate QAOA implementations for . Cirq's modular structure allows users to define custom circuits with variational parameters, enabling hybrid execution on quantum hardware or simulators. Released under the Apache 2.0 license, Cirq is part of Google's Quantum AI toolkit. Classiq is a proprietary quantum software platform that streamlines the design, synthesis, and optimization of quantum algorithms, including those for problems. Launched in 2020, it features a synthesis engine that automatically generates hardware-optimized quantum circuits from high-level functional models, reducing manual complexity. The platform offers a free tier for academic and exploratory use, supporting hybrid workflows across various quantum backends. Classiq's tools emphasize scalability for optimization in fields like and . PyQuil, Rigetti Computing's open-source Python library, enables the construction and execution of quantum programs for optimization on the Forest platform, now evolved into Quantum Cloud Services (QCS). It uses the Quil instruction set architecture (ISA) language to define quantum circuits and supports hybrid loops that alternate between quantum processing unit (QPU) execution and classical computation for iterative optimization. PyQuil facilitates variational algorithms by allowing parameter sweeps and integration with classical solvers. Licensed under Apache 2.0, it is a core component of Rigetti's SDK for quantum annealing and gate-based optimization.

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