Given a transformation between input and output values, described by a mathematical functionf, optimization deals with generating and selecting a 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 minimization problem, can be represented in the following way
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 spaceRn, 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, sets of integers.
The use of optimization software requires that the function f is defined in a suitable programming language and connected at compile 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 optimization software organized according to license and business model type.
Gurobi — integer, linear and quadratic programming
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) is a multiobjective, multidimensional nonlinear optimization technology
Kimeme — an open platform for multi-objective optimization and multidisciplinary design optimization
MIDACO-Solver — Black-Box optimization software for continuous, combinatorial and mixed integer problems. Available in Matlab, C/C++ and Fortran.
modeFRONTIER — multidisciplinary design optimization, for computer-aided engineering
Maple (software) — Linear, quadratic, and nonlinear, continuous and integer optimization. Constrained and unconstrained. Global optimization with add-on toolbox.
MATLAB — Standard and large -scale optimization problems; multiple maxima, multiple minima, and non-smooth optimization problems; estimation and optimization of model parameters.
Mathematica — large-scale multivariate constrained and unconstrained, linear and nonlinear, continuous and integer 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 optimization; continuous or integer problems.
Nexus — multidisciplinary optimization and design process integration
NMath — linear, quadratic and nonlinear programming
IOSO — multidisciplinary design optimization, for computer-aided engineering
OptimJ — Java based modeling language. Premium Edition includes support for Gurobi, Mosek and CPLEX solvers
Optimus platform — a process integration and design optimization platform developed by Noesis Solutions
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-modeling.
OptiStruct — Award-winning CAE technology for conceptual design synthesis and structural optimization.
PHX ModelCenter — a graphical environment for automation, integration, and design optimization.
PottersWheel — Parameter estimation in ordinary differential equations (Matlab toolbox, free for academic use).
Sipesc.Opt — general purpose optimization software, including GUI and script language interface.
SmartDO — multidisciplinary global design optimization, specialized in computer-aided engineering (CAE). using the direct global search approaches.
TOMLAB — TOMLAB supports global optimization, integer programming, all types of least squares, linear, quadratic and unconstrained programming for MATLAB. TOMLAB supports solvers like Gurobi, CPLEX, SNOPT and KNITRO.
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