MIP features in LP file format

MIP integer variables

This rule applies to the CPLEX MIP optimizer.

To specify any of the variables as general integer variables, add a GENERAL section; to specify any of the variables as binary integer variables, add a BINARY section. The GENERAL and BINARY sections follow the BOUNDS section, if one is present; otherwise, they follow the constraints section. Either of the GENERAL or BINARY sections can precede the other. The GENERAL section is preceded by the word GENERAL, GENERALS, or GEN in any mix of upper- and lowercase characters which must appear alone on a line. The following line or lines should list the names of all variables which are to be restricted to general integer values, separated by at least one space. The BINARY section is preceded by the word BINARY, BINARIES, or BIN in any mix of upper- and lowercase characters which must appear alone on a line. The following line or lines should list the names of all variables which are to be restricted to binary integer values, separated by at least one space. Binary variables are automatically given bounds of 0 (zero) and 1 (one), unless alternative bounds are specified in the BOUNDS section, in which case a warning message is issued.

Here is an example of a problem formulation in LP format where x4 is a general integer:

Maximize
 obj: x1 + 2 x2 + 3 x3 + x4
Subject To
 c1: - x1 + x2 + x3 + 10 x4 <= 20
 c2: x1 - 3 x2 + x3 <= 30
 c3: x2 - 3.5 x4 = 0
Bounds
 0 <= x1 <= 40
 2 <= x4 <= 3
General
 x4
End

If branching priorities or branching directions exist, enter this information through ORD files, as documented in ORD file format: priorities and branching orders.

MIP semi-continuous variables

This rule applies to the CPLEX MIP optimizer.

To specify any of the variables as semi-continuous variables, that is as variables that may take the value 0 or values between the specified lower and upper bounds, use a SEMI-CONTINUOUS section. This section must follow the BOUNDS , GENERALS , and BINARIES sections. The SEMI-CONTINUOUS section is preceded by the keyword SEMI-CONTINUOUS , SEMI , or SEMIS . The following line or lines should list the names of all the variables which are to be declared semi-continuous, separated by at least one space.

To specify a semi-integer variable, the name of the variable must be listed both in the GENERAL and the SEMI-CONTINUOUS sections.

Semi-continuous
x1 x2 x3

MIP special ordered sets

This rule applies to the CPLEX MIP optimizer. To specify special ordered sets, use an SOS section, which is preceded by the SOS keyword. The SOS section should follow the Bounds, General, Binaries and Semi-Continuous sections. Special ordered sets of type 1 require that, of the variables in the set, one at most may be nonzero. Special ordered sets of type 2 require that at most two variables in the set may be nonzero, and if there are two nonzeros, they must be adjacent. Adjacency is defined by the weights, which must be unique within a set given to the variables. The sorted weights define the order of the special ordered set. For MIP branch and cut, the order is used to decide how the variables are branched upon. See the CPLEX User’s Manual for more information. The set is specified by an optional set name followed by a colon and then either of the S1 or S2 keywords (specifying the type) followed by a double colon. The set member names are listed on this line or lines, with their weights. Variable names and weights are separated by a colon, for example:

SOS

set1: S1:: x1:10 x2:13

MIP indicator constraints

This rule applies to CPLEX MIP optimizer.

To specify an indicator constraint, enter it among any other constraints in the model, like this:

[constraintname:]  binaryvariable = value  ->  linear constraint

The constraint name, followed by a colon, is optional. The hyphen followed by the greater-than symbol (->), separates the indicator variable and its value from the linear constraint that is controlled. The indicator variable must be declared as a binary variable, and the value it is compared to must be either 0 (zero) or 1 (one).

These limitations apply to indicator constraints in LP file format:

• The constraint must be linear; a quadratic constraint is not allowed to have an indicator constraint.
• A lazy constraint cannot have an indicator constraint.
• A user-defined cut cannot have an indicator constraint.