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Integer programming is NP-complete. In particular, the special case of 0–1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. [1] If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. [2]
MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. Overview [ edit ]
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.
HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. [1] Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, R, JavaScript, Fortran, and C#. It has no external dependencies.
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. [3] OR-Tools is a set of components written in C++ but provides wrappers for Java, .NET and Python.
Convex Over and Under ENvelopes for Nonlinear Estimation (Couenne) is an open-source library for solving global optimization problems, also termed mixed integer nonlinear optimization problems. [1] A global optimization problem requires to minimize a function, called objective function, subject to a set of constraints. Both the objective ...
Single- or multi-process optimization over networks (SYMPHONY) is an open source branch and cut framework for solving mixed integer programs (MIPs) over heterogeneous networks. [9] It can use CLP, CPLEX, XPRESS or other linear programming solvers to solve the underlying linear programs.
Cutting planes were proposed by Ralph Gomory in the 1950s as a method for solving integer programming and mixed-integer programming problems. However, most experts, including Gomory himself, considered them to be impractical due to numerical instability, as well as ineffective because many rounds of cuts were needed to make progress towards the solution.