This was found somewhere online, original source is unknown. Note that not all details given below apply for our algorithms, since e.g. aolibILP forces all variables to be 0/1 integers regardless of specified ranges.

Introduction

The main things to know about MPS format are that it is column oriented (as opposed to entering the model as equations), and everything (variables, rows, etc.) gets a name.

MPS is an old format, so it is set up as though you were using punch cards, and is not free format. Fields start in column 1, 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 (like I said, MPS has long historical roots), 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; you should pick names that are meaningful to you, or will be easy for a post-processing code to read.

Example

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

NAME          TESTPROB
ROWS
 N  COST
 L  LIM1
 G  LIM2
 E  MYEQN
COLUMNS
    XONE      COST                 1   LIM1                 1
    XONE      LIM2                 1
    YTWO      COST                 4   LIM1                 1
    YTWO      MYEQN               -1
    ZTHREE    COST                 9   LIM2                 1
    ZTHREE    MYEQN                1
RHS
    RHS1      LIM1                 5   LIM2                10
    RHS1      MYEQN                7
BOUNDS
 UP BND1      XONE                 4
 LO BND1      YTWO                -1
 UP BND1      YTWO                 1
ENDATA

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

Optimize
 COST:    XONE + 4 YTWO + 9 ZTHREE
Subject To
 LIM1:    XONE + YTWO <= 5
 LIM2:    XONE + ZTHREE >= 10
 MYEQN:   - YTWO + ZTHREE  = 7
Bounds
 0 <= XONE <= 4
-1 <= YTWO <= 1
End

General

Strangely, there is nothing in MPS format that specifies the direction of optimization. And there really is no standard "default" direction; some LP codes will maximize if you don't specify otherwise, others will minimize, and still others put safety first and have no default and require you to specify it somewhere in a control program or by a calling parameter. If you have a model formulated for minimization and the code you are using insists on maximization (or vice versa), it may be easy to convert: just multiply all the coefficients in your objective function by (-1). The optimal value of the objective function will then be the negative of the true value, but the values of the variables themselves will be correct.

Any line with an asterisk (*) in Column 1 is treated as a comment. The eight character names used to specify variables, constraints and other entities are fixed format. Names are not automatically justified, so blanks are treated just like other characters. For example "ROW1 " is not the same as " ROW1 ". (Note that some optimisers do not permit blanks in names.) No case conversion is performed, so "row1 " is different from "ROW1 ".

Floating point numbers may be specified in free format within the 12 character field (including embedded blanks). The following list describes the possible ways of writing a number:

  1. Mantissa:

    1. + or -: optional sign character (no sign indicates a positive number)

    2. digits: optional integer part of the mantissa

    3. .: optional decimal point (if not present, a decimal point will be assumed after the mantissa digit)

    4. digits: optional fraction part of the mantissa -the mantissa must contain at least one digit

  2. Exponent (optional):

    1. D or E: exponent leader

    2. + or -: optional exponent sign

    3. digits: exponent digits

File structure

The NAME card can have anything you want, starting in column 15. The ROWS section defines the names of all the constraints; entries in column 2 or 3 are E for equality rows, L for less-than ( <= ) rows, G for greater-than ( >= ) rows, and N for non-constraining rows (the first of which would be interpreted as the objective function). The order of the rows named in this section is unimportant.

The largest part of the file is in the COLUMNS section, which is the place where the entries of the A-matrix are put. All entries for a given column must be placed consecutively, although within a column the order of the entries (rows) is irrelevant. Rows not mentioned for a column are implied to have a coefficient of zero.

The RHS section allows one or more right-hand-side vectors to be defined; most people don't bother having more than one. In the above example, the name of the RHS vector is RHS1, and has non-zero values in all 3 of the constraint rows of the problem. Rows not mentioned in an RHS vector would be assumed to have a right-hand-side of zero.

The optional BOUNDS section lets you put lower and upper bounds on individual variables (no * wild cards, unfortunately), instead of having to define extra rows in the matrix. All the bounds that have a given name in column 5 are taken together as a set. Variables not mentioned in a given BOUNDS set are taken to be non-negative (lower bound zero, no upper bound). A bound of type UP means an upper bound is applied to the variable. A bound of type LO means a lower bound is applied. A bound type of FX ("fixed") means that the variable has upper and lower bounds equal to a single value. A bound type of FR ("free") means the variable has neither lower nor upper bounds.

The final card must be ENDATA, and yes, it is spelled funny.

MPS_file_format (last edited 2008-03-10 19:07:37 by localhost)