MPSReader Class

Reads a linear programming problem from an MPS file.

For a list of all members of this type, see MPSReader Members.

System.Object
Imsl.Math.MPSReader

public class MPSReader

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

An MPS file defines a linear or quadratic programming problem. Linear programming problems read using this class are assumed to be of the form:

$\mathop{\min}\limits_{x\;\in\;R^n }c^T x$

subject to

$b_l \le Ax \le b_u$

$\,\,x_l \le x \le x_u$

where c is the objective coefficient vector, A is the coefficient matrix, and the vectors

, and

are the lower and upper bounds on the constraints and the variables, respectively.

The following table helps map this notation into use of MPSReader.

C	Objective
A	Constraint matrix
	Lower Range
	Upper Range
	Lower Bound
	Upper Bound

If the MPS file specifies an equality constraint or bound, the corresponding lower and upper values will be exactly equal.

The problem formulation assumes that the constraints and bounds are two-sided. If a particular constraint or bound has no lower limit, then the corresponding entry in the structure is set to negative machine infinity. If the upper limit is missing, then the corresponding entry in the structure is set to positive machine infinity.

MPS File Format

There is some variability in the MPS format. This section describes the MPS format accepted by this reader.

An MPS file consists of a number of sections. Each section begins with a name in column 1. With the exception of the NAME section, the rest of this line is ignored. Lines with a '*' or '$' in column 1 are considered comment lines and are ignored.

The body of each section consists of lines divided into fields, as follows:

Field Number	Columns	Content
1	2-3	Indicator
2	5-12	Name
3	15-22	Name
4	25-36	Value
5	40-47	Name
6	50-61	Value

The format limits MPS names to 8 characters and values to 12 characters. The names in fields 2, 3 and 5 are case sensitive. Leading and trailing blanks are ignored, but internal spaces are significant.

The sections in an MPS file are as follows:

NAME

ROWS

COLUMNS

RHS

RANGES (optional)

BOUNDS (optional)

QUADRATIC (optional)

ENDATA

Sections must occur in the above order.

MPS keywords, section names and indicator values, are case insensitive. Row, column and set names are case sensitive.

NAME Section

The NAME section contains the single line. A problem name can occur anywhere on the line after NAME and before columns 62. The problem name is truncated to 8 characters.

ROWS Section

The ROWS section defines the name and type for each row. Field 1 contains the row type and field 2 contains the row name. Row type values are not case sensitive. Row names are case sensitive. The following row types are allowed:

Row Type	Meaning
E	Equality constraint
L	Less than or equal constraint
G	Greater than or equal constraint
N	Objective of a free row

COLUMNS Section

The COLUMNS section defines the nonzero entries in the objective and the constraint matrix. The row names here must have been defined in the ROWS section.

Field	Contents
2	Column name
3	Row name
4	Value for the entry whose row and column are given by fields 2 and 3
5	Row name
6	Value for the entry whose row and column are given by fields 2 and 5

Note: Fields 5 and 6 are optional.

The COLUMNS section can also contain markers. These are indicated by the name 'MARKER' (with the quotes) in field 3 and the marker type in field 4 or 5.

Marker type 'INTORG' (with the quotes) begins an integer group. The marker type 'INTEND' (with the quotes) ends this group. The variables corresponding to the columns defined within this group are required to be integer.

RHS Section

The RHS section defines the right-hand side of the constraints. An MPS file can contain more than one RHS set, distinguished by the RHS set name. The row names here must be defined in the ROWS section.

Field	Contents
2	RHS name
3	Row name
4	Value for the entry whose row and column are given by fields 2 and 3
5	Row name
6	Value for the entry whose row and column are given by fields 2 and 5

Note: Fields 5 and 6 are optional.

RANGES Section

The optional RANGES section defines two-sided constraints. An MPS file can contain more than one range set, distinguished by the range set name. The row names here must have been defined in the ROWS section.

Field	Contents
2	Range set name
3	Row name
4	Value for the entry whose row and column are given by fields 2 and 3
5	Row name
6	Value for the entry whose row and column are given by fields 2 and 5

Note: Fields 5 and 6 are optional.

Ranges change one-sided constraints, defined in the RHS section, into two-sided constraints. The two-sided constraint for row i depends on the range value, , defined in this section. The right-hand side value, , is defined in the RHS section. The two sided constraints for row i are given in the following table:

Row Type	Lower Constraint	Upper Constraint
G
L
E

BOUNDS Section

The optional BOUNDS section defines bounds on the variables. By default, the bounds are $0\le x_i\le\infty$ . The bounds can also be used to indicate that a variable must be an integer.

More than one bound can be set for a single variable. For example, to set $2\le x_i\le 6$ use a LO bound with value 2 to set $2\le x_i$ and an UP bound with value 6 to add the condition $x_i \le 6$ .

An MPS file can contain more than one bounds set, distinguished by the bound set name.

Field	Contents
1	Bounds type
2	Bounds set name
3	Column name
4	Value for the entry whose set and column are given by fields 2 and 3
5	Column name
6	Value for the entry whose set and column are given by fields 2 and 5

Note: Fields 5 and 6 are optional.

The bound types are as follows. Here are the bound values defined in this section, the are the variables, and I is the set of integers.

Bound Type	Definintion	Formula
LO	Lower bound	$b_i\le x_i$
UP	Upper bound	$x_i\le b_i$
FX	Fixed Variable
FR	Free variable	$-\infty\le x_i\le\infty$
MI	Lower bound is minus infinity	$-\infty\le x_i$
PL	Upper bound is positive infinity	$x_i\le\infty$
BV	Binary variable (variable must be 0 or 1)	$x_i\in\{0,1\}$
UI	Upper bound and integer	$x_i\le b_i$ and $x_i\in I$
LI	Lower bound and integer	$b_i\le x_i$ and $x_i\in I$
SC	Semicontinuous	0 or $b_i\le x_i$