MPS (format)

MPS (format)
Name	MPS
Extension	.mps
Mime	application/octet-stream
Owner	IBM
Released	1970s
Genre	data interchange

MPS (format) is a data file format originally designed for representing mathematical programming and operations research models. It serves as an exchange medium between modeling systems and solvers, enabling interoperability among commercial and academic tools. The format became a de facto standard in benchmarking and solver development, used in contexts ranging from linear programming competitions to industrial optimization projects.

Overview

The format encodes models using a line-oriented, column-based textual representation that maps variables, constraints, coefficients, and bounds into named sections. It has been adopted by institutions and projects including IBM, Bell Labs, AT&T, MIT, Stanford University, Carnegie Mellon University, Princeton University, University of California, Berkeley, University of Illinois Urbana–Champaign, ETH Zurich, INRIA, CNRS, University of Oxford, University of Cambridge, Imperial College London, National University of Singapore, Tsinghua University, Peking University, University of Tokyo, Kyoto University, Seoul National University, KTH Royal Institute of Technology, TU Delft, Delft University of Technology, University of Melbourne, University of Sydney, University of Toronto, McGill University, University of British Columbia, Los Alamos National Laboratory, Sandia National Laboratories, Argonne National Laboratory, NASA, European Space Agency, Siemens, Honeywell, General Electric, Ford Motor Company, Boeing, Airbus, Shell plc, BP, ExxonMobil, Goldman Sachs, J.P. Morgan, Morgan Stanley, McKinsey & Company, Boston Consulting Group, Accenture, Oracle Corporation, and Microsoft for exchanging benchmark instances and solver inputs. Its terse structure favors portability across platforms such as UNIX, MS-DOS, Windows NT, VAX/VMS, IBM AIX, HP-UX, Solaris (operating system), and Linux.

History and Development

The format emerged in the 1960s–1970s era of operations research where exchanges between early solvers like CPLEX, Simplex implementations, and in-house codes at IBM and university groups required a common notation. Early adopters included research teams behind NETLIB, AMPL, GAMS, LINGO, and academic benchmarks from Stanford Linear Programming Group and Princeton Numerical Analysis. Over time the format was influenced by standards work at organizations such as IEEE and by datasets distributed via Bellcore, Mathematical Programming Society, and archives maintained by Cornell University and Argonne National Laboratory. Major solver vendors—IBM ILOG CPLEX, FICO Xpress, Gurobi Optimization, Mosek, GLPK, CBC, and SCIP—provided import/export support, while academic tools like COIN-OR projects and NEOS Server used it for remote submission and benchmarking.

File Format Specification

The specification uses named card sections such as NAME, ROWS, COLUMNS, RHS, BOUNDS, and ENDATA with fixed-column semantics left over from punch-card conventions. Rows define constraint types (E, L, G, N) and names; columns list variable contributions to rows with coefficients; RHS sections supply right-hand-side values; BOUNDS map variables to bound types (UP, LO, FX, FR, MI, PL); integer variables are sometimes signaled in separate indicator files for integer programming. Implementations frequently rely on conventions from ISO/IEC-era textual formats and mimic features seen in datasets from NETLIB and problem libraries circulated at Bell Labs and Argonne National Laboratory. Extensions and vendor-specific annotations add sections for ranges, quadratic terms, and SOS (special ordered sets) used by solvers like CPLEX and Gurobi Optimization.

Tools and Implementations

Conversion and parsing libraries exist across languages and ecosystems: C/C++ parsers in projects such as COIN-OR, Fortran readers in legacy solvers from IBM, Java bindings in tools like OptaPlanner and Apache Commons Math, Python loaders in SciPy, Pyomo, PuLP, and OR-Tools bindings from Google; MATLAB and R toolboxes provide import routines used at MIT, Stanford University, and ETH Zurich. Many integrated modeling environments—AMPL, GAMS, LINGO, JuMP, and CVX—support MPS export. Benchmarking services such as NEOS Server and repositories like NETLIB and MIPLIB distribute MPS instances; graphical modelers and IDEs in Eclipse, Visual Studio, and Jupyter ecosystems leverage converters to display models.

Applications and Use Cases

The format is widely used for linear programming, mixed-integer programming, and quadratic programming instances in academic research, industrial scheduling, supply chain design, portfolio optimization, network flow problems, and energy systems planning. Fields and projects employing MPS instances include studies by NASA on trajectory optimization, European Space Agency mission planning, Siemens industrial scheduling, Ford Motor Company production planning, Goldman Sachs risk analytics, BP and Shell plc reservoir planning, and computational benchmarks in competitions like the International Mathematical Olympiad-adjacent modeling challenges and solver contests hosted by Mathematical Optimization Society.

Compatibility and Interoperability

Interoperability relies on conservative parsing rules to handle varying dialects created by different vendors and archives; common issues include column misalignment, vendor-specific sections, and extended annotations for quadratic or SOS terms. Conversion tools and translators maintained by communities around COIN-OR, NEOS Server, NETLIB, and academic centers at MIT, Stanford University, Princeton University, and ETH Zurich help bridge differences. Modern interchange increasingly complements MPS with formats like LP format, MathML, JSON-based model schemas, and solver APIs from Gurobi Optimization, IBM ILOG CPLEX, and Google OR-Tools to address needs not met by the original, punch-card-oriented design.

Category:File formats