MPSReader (JMSL Numerical Library (jmsl) 2021.0.0 API)

java.lang.Object
- com.imsl.io.MPSReader

All Implemented Interfaces:: Serializable

public class MPSReader
extends Object
implements Serializable

Reads a linear programming problem from an MPS file.

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 $b_l$, $b_u$, $x_l$, and $x_u$ are the lower and upper bounds on the constraints and the variables, respectively.

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

C	Objective
A	Constraint matrix
$b_l$	Lower Range
$b_u$	Upper Range
$x_l$	Lower Bound
$x_u$	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, $r_i$, defined in this section. The right-hand side value, $b_i$ , 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	$b_i$	$b_i + \|r_i\|$
L	$b_i - \|r_i\|$	$b_i$
E	$b_i + min(0, r_i)$	$b_i + max(0, r_i)$

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 $b_i$ are the bound values defined in this section, the $x_i$ 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	$x_i = b_i$
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 $b_i \le x_i$

The bound type names are not case sensitive.

If the bound type is UP or UI and $b_i \le x_i$ then the lower bound is set to $-\infty$.

ENDATA Section

The ENDATA section ends the MPS file.

See Also:: Example, Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static class`	`MPSReader.Element` An element in the sparse contraint matrix.
`static class`	`MPSReader.InvalidMPSFileException` The MPS file is invalid.
`class`	`MPSReader.Row` A row either in the constraint matrix or a free row.

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`BINARY_VARIABLE` Variable must be either 0 or 1.
`static int`	`CONTINUOUS_VARIABLE` Variable is a real number.
`static int`	`INTEGER_VARIABLE` Variable must be an integer.

Constructor Summary

Constructors
Constructor and Description

MPSReader()

Constructors
Constructor and Description
`MPSReader()`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`getLowerBound(int iVariable)` Returns the lower bound for a variable.
`double`	`getLowerRange(int iRow)` Returns the lower range value for a constraint equation.
`String`	`getName()` Returns the name of the MPS problem.
`String`	`getNameBounds()` Returns the name of the BOUNDS set.
`String`	`getNameColumn(int iColumn)` Returns the name of a constraint column.
`String`	`getNameObjective()` Returns the name of the free row containing the objective.
`String`	`getNameRanges()` Returns the name of the RANGES set.
`String`	`getNameRHS()` Returns the name of the RHS section.
`String`	`getNameRow(int iRow)` Returns the name of a contraint row.
`int`	`getNumberOfBinaryConstraints()` Returns the number of binary constraints.
`int`	`getNumberOfColumns()` Returns the number of columns in the constraint matrix.
`int`	`getNumberOfIntegerConstraints()` Returns the number of integer constraints.
`int`	`getNumberOfNonZeros()` Returns the number of nonzeros in the constraint matrix.
`int`	`getNumberOfRows()` Returns the number of rows in the constraint matrix.
`MPSReader.Row`	`getObjective()` Returns the objective as a Row.
`double[]`	`getObjectiveCoefficients()` Returns the coefficents of the objective row.
`MPSReader.Row`	`getRow(int iRow)` Returns a row of the constraint matrix or a free row.
`double[]`	`getRowCoefficients(int iRow)` Returns the coefficents of a row.
`int`	`getTypeVariable(int iVariable)` Returns the type of a variable.
`double`	`getUpperBound(int iVariable)` Returns the upper bound for a variable.
`double`	`getUpperRange(int iRow)` Returns the upper range value for a constraint equation.
`protected String`	`processCommand(String command, String line)` Process a section of the MPS file.
`void`	`read(Reader reader)` Reads and parses the MPS file.
`void`	`setNameBounds(String nameBounds)` Sets the name of the BOUNDS set to be used.
`void`	`setNameObjective(String nameObjective)` Sets the name of the free row containing the objective.
`void`	`setNameRanges(String nameRanges)` Sets the name of the RANGES set to be used.
`void`	`setNameRHS(String nameRHS)` Sets the name of the RHS set to be used.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - CONTINUOUS_VARIABLE
```
public static final int CONTINUOUS_VARIABLE
```
    Variable is a real number.
    
    See Also:
    
    Constant Field Values
  - INTEGER_VARIABLE
```
public static final int INTEGER_VARIABLE
```
    Variable must be an integer.
    
    See Also:
    
    Constant Field Values
  - BINARY_VARIABLE
```
public static final int BINARY_VARIABLE
```
    Variable must be either 0 or 1.
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - MPSReader
```
public MPSReader()
```
- Method Detail
  - read
```
public void read(Reader reader)
          throws IOException,
                 MPSReader.InvalidMPSFileException
```
    Reads and parses the MPS file.
    
    Throws:
    
    IOException
    
    MPSReader.InvalidMPSFileException
  - processCommand
```
protected String processCommand(String command,
                                String line)
                         throws IOException,
                                MPSReader.InvalidMPSFileException
```
    Process a section of the MPS file.
    
    Returns:
    
    the next line to be processed. This line was read, but was not part of the section being processed.
    
    Throws:
    
    IOException
    
    MPSReader.InvalidMPSFileException
  - getName
```
public String getName()
```
    Returns the name of the MPS problem. This is the value of the NAME field.
  - getObjective
```
public MPSReader.Row getObjective()
```
    Returns the objective as a Row.
  - getObjectiveCoefficients
```
public double[] getObjectiveCoefficients()
```
    Returns the coefficents of the objective row.
  - getNumberOfRows
```
public int getNumberOfRows()
```
    Returns the number of rows in the constraint matrix.
  - getNumberOfColumns
```
public int getNumberOfColumns()
```
    Returns the number of columns in the constraint matrix.
  - getNumberOfNonZeros
```
public int getNumberOfNonZeros()
```
    Returns the number of nonzeros in the constraint matrix.
  - getNumberOfIntegerConstraints
```
public int getNumberOfIntegerConstraints()
```
    Returns the number of integer constraints. An integer constraint is the requirment that a variable be an integer.
  - getNumberOfBinaryConstraints
```
public int getNumberOfBinaryConstraints()
```
    Returns the number of binary constraints. An binary constraint is the requirment that a variable be either 0 or 1. Binary constraints are also integer contraints.
  - getLowerRange
```
public double getLowerRange(int iRow)
```
    Returns the lower range value for a constraint equation.
    
    Parameters:
    
    iRow - is the row number of the equation.
  - getUpperRange
```
public double getUpperRange(int iRow)
```
    Returns the upper range value for a constraint equation.
    
    Parameters:
    
    iRow - is the row number of the equation.
  - getLowerBound
```
public double getLowerBound(int iVariable)
```
    Returns the lower bound for a variable.
    
    Parameters:
    
    iVariable - is the number of the variable.
  - getUpperBound
```
public double getUpperBound(int iVariable)
```
    Returns the upper bound for a variable.
    
    Parameters:
    
    iVariable - is the number of the variable.
  - getTypeVariable
```
public int getTypeVariable(int iVariable)
```
    Returns the type of a variable. The variable types are CONTINUOUS_VARIABLE, BINARY_VARIABLE or INTEGER_VARIABLE.
    
    Parameters:
    
    iVariable - is the number of the variable.
  - setNameObjective
```
public void setNameObjective(String nameObjective)
```
    Sets the name of the free row containing the objective. An MPS file can contain free rows, but only one is retained by this reader as the objective. If not set name is set, then the first free row in the file is used as the objective.
  - getNameObjective
```
public String getNameObjective()
```
    Returns the name of the free row containing the objective.
  - setNameRHS
```
public void setNameRHS(String nameRHS)
```
    Sets the name of the RHS set to be used. An MPS file can contain multiple sets of RHS values, but only one is retained by this reader. If not set name is set, then the first set in the file is used.
  - getNameRHS
```
public String getNameRHS()
```
    Returns the name of the RHS section.
  - setNameRanges
```
public void setNameRanges(String nameRanges)
```
    Sets the name of the RANGES set to be used. An MPS file can contain multiple sets of RANGES, but only one is retained by this reader. If not set name is set, then the first set in the file is used.
  - getNameRanges
```
public String getNameRanges()
```
    Returns the name of the RANGES set. An MPS file can contain multiple sets of RANGES, but only one is retained by this reader. Returns null if there is no RANGES set.
  - setNameBounds
```
public void setNameBounds(String nameBounds)
```
    Sets the name of the BOUNDS set to be used. An MPS file can contain multiple sets of BOUNDS, but only one is retained by this reader. If not set name is set, then the first set in the file is used.
  - getNameBounds
```
public String getNameBounds()
```
    Returns the name of the BOUNDS set. An MPS file can contain multiple sets of BOUNDS, but only one is retained by this reader. Returns null if there is no BOUNDS set.
  - getNameRow
```
public String getNameRow(int iRow)
```
    Returns the name of a contraint row.
  - getNameColumn
```
public String getNameColumn(int iColumn)
                     throws MPSReader.InvalidMPSFileException
```
    Returns the name of a constraint column. Constraint column names are also variable names.
    
    Parameters:
    
    iColumn - is the number of the column.
    
    Throws:
    
    MPSReader.InvalidMPSFileException
  - getRow
```
public MPSReader.Row getRow(int iRow)
```
    Returns a row of the constraint matrix or a free row.
    
    Parameters:
    
    iRow - is the number of the row.
  - getRowCoefficients
```
public double[] getRowCoefficients(int iRow)
```
    Returns the coefficents of a row.
    
    Parameters:
    
    iRow - is the number of the row.

Row Type	Lower Constraint	Upper Constraint
G	\(b_i\)	\(b_i + \|r_i\|\)
L	\(b_i - \|r_i\|\)	\(b_i\)
E	\(b_i + min(0, r_i)\)	\(b_i + max(0, r_i)\)

C	Objective
A	Constraint matrix
\(b_l\)	Lower Range
\(b_u\)	Upper Range
\(x_l\)	Lower Bound
\(x_u\)	Upper Bound

Class MPSReader

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

CONTINUOUS_VARIABLE

INTEGER_VARIABLE

BINARY_VARIABLE

Constructor Detail

MPSReader

Method Detail

read

processCommand

getName

getObjective

getObjectiveCoefficients

getNumberOfRows

getNumberOfColumns

getNumberOfNonZeros

getNumberOfIntegerConstraints

getNumberOfBinaryConstraints

getLowerRange

getUpperRange

getLowerBound

getUpperBound

getTypeVariable

setNameObjective

getNameObjective

setNameRHS

getNameRHS

setNameRanges

getNameRanges

setNameBounds

getNameBounds

getNameRow

getNameColumn

getRow

getRowCoefficients