LP-Testcases
The classical collection of mostly real-life problems is at NETLIB. The files are compressed with a special utility (MPC), they need to be uncompressed using EMPS. Then they are in MPS-format. The original source for the files and the (un)compress utilities is netlib. See the README. One can also retrieve the files in AMPL-format from NETLIB_AMPL. A comprehensive archive for files in different formats is the COAP collection.
Here is another large collection of mpc-compressed MPS files and here and here are some additional files.
In practice often some or all of the variables are constrained to be integer valued. Here is a collection of mixed integer linear programming problems:
Testcases for MILP
| MIPLIB 2017 (MPS format) | |
| MILPlib (MPS format) | MILPlib (AMPL format) |
| Coral MIPlib (MPS format) | |
| Alper Atamtürk's Collection (MPS format) | |
| UniBo (MPS format) | difficult cases from U Bologna |
Testcases for MIQP and MIQCP
| QPlib (multiple formats) | Both convex, non convex, continuous, discrete instances |
| MIQPlib (ext MPS format) | |
| MIQPlib (AMPL format) |
Stochastic Programming Testcases
in SMPS format
| Sampling Methods for SP |
| POSTS (POrtable Stochastic programming Test Set) |
| Stochastic Integer Programming Test Problem Library |
| Another testset from various applications |
Testcases for transportation problems
| Fixed Charge Transportation Benchmark | MPS format |
Testcases for unconstrained minimization
| Wikipedia's list | some global test problems, also multiobjective |
| Matlab m-files | many global test problems |
| Test Problems for nonsmooth optimization | large and small scale instances |
| PSARNOT | a test set for evaluating methods for nonsmooth optimization |
| Testcases for unconstrained optimization codes | collected by Buckley |
| Testcases for unconstrained optimization codes | generators by Nielsen (Matlab) |
| The More-Garbow-Hillstrom collection | providing first and second derivatives |
| The More-Garbow-Hillstrom collection | in Matlab |
| The GKLS generator | includes RNG, docs (C) |
| Global trajectory optimization problems | Matlab/C++/Python |
There are more codes for unconstrained problems in the general collections listed below.
Testcases for nonlinear systems of equations and nonlinear least squares problems
| Netlib/Minpack | dense problems |
| Coprin bench page | small polynomial and nonpolynomial systems |
| Luksan's test problems | sparse problems; also others |
| polynomial systems | with results for PHCpack |
Testcases for QP
| convex QP testproblems | in extended MPS format or here or in AMPL format |
| JCastro | Some of these problems are QPs in MPS or AMPL NL format |
| QPlib (multiple formats) | Both convex, non convex, continuous, discrete instances |
| Benchmark examples for the OSQP solver | some benchmark instances and scripts to compare QP solvers |
Testcases for semidefinite and second-order cone programming
| CBLIB | Conic Benchmark Library with new format and conversion scripts (incl discrete problems) |
| SDPLIB | SDP test problems in sparse SDPA-format |
| SQL | SQL problems (DIMACS Challenge), SeDuMi and DIMACS graph formats, in sparse SDPA format |
| SOTIROV | A new library of structured semidefinite programming instances (sparse SDPA format) |
| RDM | Semidefinite programming instances from quantum chemistry (sparse SDPA format) |
| KOCVARA | sparse SDPs from structural optimization (in sparse SDPA and Matlab binary format) |
| QAP | SDP relaxations of QAP problems by Rendl, Sotirov, and Wolkowicz (in sparse SDPA and Matlab binary format) |
| SOCP | Second-order cone problems from 7th DIMACS Challenge (in extended MPS format) |
| SDP | More SDP problems (in sparse SDPA and SeDuMi format) |
| COMPlib | a collection of test examples for nonlinear semidefinite programs, control system design and related problems |
Testcases for general nonlinear Programming
The following collection is written in standard f77 with milstd1753 extensions. It uses a problem formulation for nonlinear programming f(x)=min subject to h(x)=0 and g(x)>=0, where h and g are general smooth vector functions. there is also an interface for the format used e.g. by codes like NPSOL, MINOS and SNOPT. The collection contains all examples of the two collections assembled by Schittkowski resp. Hock and Schittkowski, most of Himmelblau and Dembo and some additional ones. The code DONLP2 solves them all but (purposely) one successfully.
| testcases for sparse and nonsmooth optimization, including nonlinear systems of equations |
Testcases for PDE constrained optimization
| Elliptic and parabolic cases | coded in AMPL |
| OPTPDE | Mathematical description and references |
Testcases for parameter estimation
| 1300 test problems from data fitting, system identification, nonlinear regression |
Testcases for various discrete optimization problems
| Biq Mac Library | Binary Quadratic and Max Cut Library |
| Multicommodity problems | problems, generators, format converter (C++) |
| Capacited Linear Multicommodity Flow Problems | problems, generators, format converter (C++) |
| frequency assignment problems | benchmarks, other info on FAP |
| traffic assignment problems | info on previously used testproblems |
| TSPLIB | library of traveling salesman, Hamiltonian cycle, sequential ordering, and capacitated vehicle routing problems |
| LOLIB | library of linear ordering problems |
| UNIBO | extensive library of codes and instances |
| VRPTW | VRPTW Benchmark Problems |
| QAPLIB | QAP Library and related links |
| SATLIB | SAT benchmarks, solvers, links etc. |
| SATlive | SAT benchmarks, solvers, links etc., updated |
| SAT Competition Web Page | annual evaluation with many examples |
| BHOSLIB | Benchmarks with hidden optimum solutions for graph problems |
| CSPLIB | a problem library for constraints |
| SteinLib | a collection of Steiner tree problems in graphs |
| PSPLIB | Project Scheduling Library |
| Taillard's instances | QAP, Scheduling, VRP |
| OR-Library | testdata for a variety of OR problems |
| 0-1 Constraint Satisfaction Benchmarks | realistic cases in various formats |
The error free formulation of large probems by direct coding in some programming language is fatiguing. Special coding devices are of great help here. The SIF (=standard input format) developed by Conn, Gould and Toint is one of them. The following collection contains nearly a thousand problems (with the additional possibility to vary dimension) coded in SIF. The selection tool allows you to extract subcollections of specific properties.
Testcases coded in special format
| CUTEst | Constrained and Unconstrained Testing Environment including large scale testcases, in SIF format |
| Libopt | environment for testing solvers on heterogeneous collections of problems |
AMPL and GAMS are modelling languages which allow a user to formulate problems in terms very near the original problem and transform this into a format required by specific solvers via specialized interfaces of which no knowledge is required by the user. They also provide automatically analytic derivatives.
| Our AMPL collection | files for various optimization problems |
| COCONUT Benchmark | NLPs and constraint satisfaction problems |
| AMPL models and interfaces | the collection at netlib |
| AMPL model files | R. Vanderbei's collection |
| COPS | Large-Scale Nonlinearly Constrained Optimization Problems (22 documented examples as AMPL models, 17 also in GAMS) |
| polynomial MIP problems | PIP, ZIMPL, GAMS, AMPL formats |
| MINLPLIB | various formats, includes other libraries |
| MINLP testproblems | AMPL format |
| MP's with equilibrium constraints | AMPL format |
| Equilibrium problems with equilibrium constraints | AMPL format |
| Multiobjective Optimization Testproblems | AMPL format |
