Linear programming (LP), also called linear optimization, is a method to achieve the best outcome in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming.
In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in the feasible region.
AMPL is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing . It was developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories. AMPL supports dozens of solvers, both open source and commercial software, including CBC, CPLEX, FortMP, MOSEK, MINOS, IPOPT, SNOPT, KNITRO, and LGO. Problems are passed to solvers as nl files. AMPL is used by more than 100 corporate clients, and by government agencies and academic institutions.
IBM ILOG CPLEX Optimization Studio is an optimization software package.
MPS is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems.
ECLiPSe is a software system for the development and deployment of constraint logic programming applications, e.g., in the areas of optimization, planning, scheduling, resource allocation, timetabling, transport, etc. It is also suited for teaching most aspects of combinatorial problem solving, e.g., problem modeling, constraint programming, mathematical programming, and search techniques. It contains constraint solver libraries, a high-level modeling and control language, interfaces to third-party solvers, an integrated development environment and interfaces for embedding into host environments.
MINTO is an integer programming solver which uses branch and bound algorithm.
CHIP is a constraint logic programming language developed by M. Dincbas, Pascal Van Hentenryck and colleagues in 1985 at the European Computer-Industry Research Centre (ECRC), initially using a Prolog language interface. It was the first programming language to implement constraint programming over finite domains, and subsequently to introduce the concept of global constraints.
In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an optimization model. Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as in ordinary mixed integer programming. Knowing that a variable is part of a set and that it is ordered gives the branch and bound algorithm a more intelligent way to face the optimization problem, helping to speed up the search procedure. The members of a special ordered set individually may be continuous or discrete variables in any combination. However, even when all the members are themselves continuous, a model containing one or more special ordered sets becomes a discrete optimization problem requiring a mixed integer optimizer for its solution.
Computational Infrastructure for Operations Research (COIN-OR), is a project that aims to "create for mathematical software what the open literature is for mathematical theory." The open literature provides the operations research (OR) community with a peer-review process and an archive. Papers in operations research journals on mathematical theory often contain supporting numerical results from computational studies. The software implementations, models, and data used to produce the numerical results are typically not published. The status quo impeded researchers needing to reproduce computational results, make fair comparisons, and extend the state of the art.
The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
LEMON is an open source graph library written in the C++ language providing implementations of common data structures and algorithms with focus on combinatorial optimization tasks connected mainly with graphs and networks. The library is part of the COIN-OR project.
ILOG S.A. was an international software company purchased and incorporated into IBM announced in January, 2009. It created enterprise software products for supply chain, business rule management, visualization and optimization. The main product line for Business Rules Management Systems (BRMS) has been rebranded as IBM Operational Decision Management. Many of the related components retain the ILOG brand as a part of their name.
FortSP is a software package for solving stochastic programming (SP) problems. It solves scenario-based SP problems with recourse as well as problems with chance constraints and integrated chance constraints. FortSP is available as a standalone executable that accepts input in SMPS format and as a library with an interface in the C programming language.
OptimJ is an extension for Java with language support for writing optimization models and abstractions for bulk data processing. The extensions and the proprietary product implementing the extensions were developed by Ateji which went out of business in September 2011. OptimJ aims at providing a clear and concise algebraic notation for optimization modeling, removing compatibility barriers between optimization modeling and application programming tools, and bringing software engineering techniques such as object-orientation and modern IDE support to optimization experts.
The Zuse Institute Berlin is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany.
Pyomo is a collection of Python software packages for formulating optimization models.
Optimization Programming Language (OPL) is an algebraic modeling language for mathematical optimization models, which makes the coding easier and shorter than with a general-purpose programming language. It is part of the CPLEX software package and therefore tailored for the IBM ILOG CPLEX and IBM ILOG CPLEX CP Optimizers. The original author of OPL is Pascal Van Hentenryck.
Google OR-Tools is a free and open-source software suite developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP), and related optimization problems.
