Comparison of optimization software
Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of a best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process. Many real-world and theoretical problems may be modeled in this general framework. 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, or the inputs can describe the configuration of a physical system and the output can be its energy.
An optimization 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 ("minimization").
Typically, 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. Maximization can be reduced to minimization by multiplying the function by minus one.
The use of optimization software requires that the function f is defined in a suitable programming language and linked 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). 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 comparison of notable optimization software libraries, either specialized or general purpose libraries with significant optimization coverage.
|Name||Language||Latest stable version||Academic/noncommercial
use is free
|Can be used in
|ALGLIB||C++, C#, FreePascal, VBA||3.8.0 / August 2013||Yes||Yes||Dual (Commercial, GPL)||General purpose library, includes optimization package.|
|AMPL||C||October 2013||Yes||Yes||Dual (Commercial, academic)||A popular algebraic modeling language for linear, mixed-integer and nonlinear optimization. Student and AMPL for courses versions are available for free.|
|APMonitor||Fortran, C++, Python, Matlab, Julia||0.6.2 / March 2016||Yes||Yes||Dual (Commercial, academic)||A differential and algebraic modeling language for mixed-integer and nonlinear optimization. Freely available interfaces for Matlab, Python, and Julia.|
|Artelys Knitro||C, C++, Python, Java, C#, Matlab, R||10.1 / April 2016||No||Yes||Proprietary||General purpose library, specialized in nonlinear optimization. Handles mixed-integer problems (MINLP) and mathematical programs with equilibrium constraints (MPEC). Specialized algorithms for nonlinear least squares problems.|
|FICO Xpress||Mosel, BCL, C, C++, Java, R Python, Matlab, .Net, VB6||8.5 / Aug 2018||Yes||Yes||Commercial, academic, community, trial||Suite of Optimization Technologies and Solutions. Includes: Solver technologies including (LP (Simplex & Barrier), MIP, MIQP, MIQCQP, MISOCP, MINLP QP, QCQP, SOCP, NLP (SLP & Interior Point); An algebraic modelling and procedural programming language; an Integrated Development Environment; Supports for a range of execution services; Support for packaging of optimization models and services as software solutions|
|GNU Linear Programming Kit||C||4.52 / July 2013||Yes||No||GPL||Free library for linear programming (LP) and mixed integer programming (MIP).|
|GNU Scientific Library||C||1.16 / July 2013||Yes||No||GPL||Free library provided by GNU project.|
|IMSL Numerical Libraries||C, Java, C#, Fortran, Python||many components||No||Yes||Proprietary|
|LIONsolver||C++, Java||2.0.198 / October 2011||Yes||Yes||Proprietary||Support for interactive and learning optimization,
according to RSO principles .
|MKL||C++, Fortran||11.1 / October 2013||No||Yes||Proprietary||Numerical library from Intel. MKL is specialized on linear algebra,|
but contains some optimization-related functionality.
|NAG Numerical Libraries||C, Fortran||Mark 26 / October 2017||No||Yes||Proprietary|
|NMath||C#||5.3 / May 2013||No||Yes||Proprietary||C# numerical library built on top of MKL.|
|OptaPlanner||Java||6.0.1.Final / Dec 2013||Yes||Yes||ASL||Lightweight optimization solver in Java|
|SciPy||Python||0.13.1 / November 2013||Yes||Yes||BSD||General purpose numerical and scientific computing library for Python.|