MPS (format)

MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems.

The format was named after an early IBM LP product and has emerged as a de facto standard ASCII medium among most of the commercial LP solvers. Essentially all commercial LP solvers accept this format, and it is also accepted by the open-source COIN-OR system. Other software may require a customized reader routine in order to read MPS files. However, with the acceptance of algebraic modeling languages MPS usage has declined. For example, according to the NEOS server statistics in January 2011 less than 1% of submissions were in MPS form compared to 59.4% of AMPL and 29.7% of GAMS submissions.

MPS is column-oriented (as opposed to entering the model as equations), and all model components (variables, rows, etc.) receive names. MPS is an old format, so it is set up for punch cards: Fields start in column 2, 5, 15, 25, 40 and 50. Sections of an MPS file are marked by so-called header cards, which are distinguished by their starting in column 1. Although it is typical to use upper-case throughout the file for historical reasons, many MPS-readers will accept mixed-case for anything except the header cards, and some allow mixed-case anywhere. The names that you choose for the individual entities (constraints or variables) are not important to the solver; one should pick meaningful names, or easy names for a post-processing code to read.

Here is a little sample model written in MPS format (explained in more detail below):

For comparison, here is the same model written out in an equation-oriented format:

As mentioned below, the lower bound on XONE is either zero or -infinity, depending upon implementation, because it is not specified. Strangely, nothing in MPS format specifies the direction of optimization, and there is no standard "default" direction; some LP solvers will maximize if not instructed otherwise, others will minimize, and still others put safety first and have no default and require a selection somewhere in a control program or by a calling parameter. If the model is formulated for minimization and the solver requires maximization (or vice versa), it is easy to convert between the two by negating all coefficients of the objective function. The optimal value of the objective function will then be the negative of the original optimal value, but the values of the variables themselves will be correct. Some programs support specifying minimization/maximization within the MPS file.

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