Find your next solver

Course about advanced modeling for discrete optimization, covering topics such as debugging or predicates

Learn more about how AI is changing businesses and how you can leverage it: Insights, tools, tips, and expert voices

Blog with news from the Operations Research and Optimization group at Amazon

Optimization Expert | Algorithm Design | Operations Research

Prof Marco Lubbecke talks about optimization in a TED Talk.

An arcade-style TSP challenge game written for https://github.com/tunnuz/arcadetsp's 2018 Christmas Party, follow the in-game instructions.

Course about basic modeling for discrete optimization with MiniZinc

The CG:SHOP Challenge (Computational Geometry: Solving Hard Optimization Problems) is an annual competition dedicated to tackling specific, difficult geometric optimization problems. Originally established as a workshop at Computational Geometry Week (CG Week) in 2019, the Challenge provides a unique platform where the success of proposed solutions is measured based on computational performance on a set of carefully selected benchmark instances. This focus on empirical evaluation marks a shift from traditional computational geometry research, which often emphasizes theoretical approaches.

An introduction to algorithms and computational complexity to solve combinatorial optimization problems

A mathematical optimization solver for large-scale optimization problems. It is independently developed by Cardinal Operations, and it includes high-performance solvers for LP, MIP, SDP, (MI)SOCP, convex (MI)QP, convex (MI)QCP and exponential cone programming.

The IBM ILOG CPLEX Optimizer solves integer programming problems, very large[3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).

Challenges from the Center for Discrete Mathematics and Theoretical Computer Science

The HiGHS Discord server.

Journal covering algorithmic and applied areas of discrete mathematics

Course about discrete optimization covering a wide range of optimization techniques such as Constraint Programming, Local Search or Column Generation

The FICO Xpress optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts. Xpress includes a general purpose non-linear solver, Xpress NonLinear, including a successive linear programming algorithm (SLP, first-order method), and Artelys Knitro (second-order methods).

GCG is a generic decomposition solver for mixed-integer programs (MIPs). It automatically performs a Dantzig-Wolfe reformulation and runs a full-fledged branch-price-and-cut algorithm to solve it to optimality. Alternatively, GCG is able to automatically apply a Benders decomposition.

For solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library.

Gurobi Optimizer is a prescriptive analytics platform and a decision-making technology developed by Gurobi Optimization, LLC. The Gurobi Optimizer (often referred to as simply, “Gurobi”) is a solver, since it uses mathematical optimization to calculate the answer to a problem.

Blog with news from Gurobi, the company behind one of the most important solvers globally

Use cases from Gurobi

HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models.

To solve a sparse symmetric system of linear equations.

Optimization software that leverages machine learning to provide unparalleled performance.

Reader in Mathematics at the University of Edinburgh

The 2026 Land-Doig MIP Competition is a computational competition hosted by the 2026 Mixed Integer Programming Workshop, offering an opportunity for teams to showcase their practical and computational prowess and fostering innovation in computational MIP. It is named in honor of Ailsa H. Land and Alison G. Harcourt (née Doig), who proposed the first LP-based branch-and-bound algorithm.

Interactive resources to learn Graph Theory.

LINGO includes a set of built-in solvers to tackle a wide variety of problems. Unlike many modeling packages, all of the LINGO solvers are directly linked to the modeling environment.

A Mixed Integer Linear Programming (MILP) solver.

Professor of operations research at RWTH Aachen University.

Practical AI for business, my experience starting and selling a company, and other content.

An extensible framework for solving discrete optimization problems using a combination of Mixed-Integer Linear Programming (MIP) and Machine Learning (ML). MIPLearn uses ML methods to automatically identify patterns in previously solved instances of the problem, then uses these patterns to accelerate the performance of conventional state-of-the-art MIP solvers such as CPLEX, Gurobi or XPRESS.

Introduction to the field of mathematical optimization.

A discussion about books focused on duality theory

This book offers an up-to-date description of relaxation/approximation and decomposition techniques, demonstrating how their combined use efficiently solves large-scale optimization problems relevant to engineering, particularly in electrical, and industrial engineering, with a focus on energy.

An interesting book about Column Generation to tackle large-scale optimization problems

Challenge from Parameterized Algorithms and Computational Experiments Challenge to bridge the gap between theory and practice of algorithms

Instances for Quadratic Assignment Problems.

SBB is a GAMS solver for Mixed Integer Nonlinear Programming (MINLP) models. It is based on a combination of the standard Branch and Bound (B&B) method known from Mixed Integer Linear Programming and some of the standard NLP solvers already supported by GAMS. SBB can use all GAMS NLP solvers as subsolvers but it works best with NLP solvers that can utilize a near optimal point as a starting point like Conopt, Minos, and Snopt.SBB supports all types of discrete variables supported by GAMS, including Binary, Integer, Semicont, Semiint, Sos1, and Sos2.

SCIP is currently one of the fastest non-commercial solvers for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP). It is also a framework for constraint integer programming and branch-cut-and-price.

SHOT (Supporting Hyperplane Optimization Toolkit) is a deterministic solver for mixed-integer nonlinear programming problems (MINLPs). Originally, SHOT was intended for convex MINLP problems only, but now also has functionality to solve nonconvex MINLP problems as a heuristic method without providing any guarantees of global optimality. SHOT can solve certain nonconvex problem types to global optimality as well.

SNDlib is a library of data for Survivable fixed telecommunication Network Design. Its purpose is to provide data about realistic telecommunication networks (including traffic) available to the research community.

Course about solving discrete optimization problems with different techniques: Constraint Programming, Mixed Integer Programming and Local Search

Learn about cutting planes in an adictive way.

Mathematical Optimization Researcher, Teacher, and Manager

Another game with map visualizations for the TSP.

Solve the TSP in a visual way from the Productions and Operations Management (Universitat Wein).

TSPLIB is a library of sample instances for the TSP (and related problems) from various sources and of various types.

Professor Emeritus, Princeton University/ Co-Founder, Optimal Dynamics, shares knowledge about sequential decision problems.