Selecting Constraints and Variables for a Math Program Declaration

A sample declaration of a math program is shown below.

MathematicalProgram Sample_Math_Program {
   Objective: ObjFunc;
   Direction: minimize;
   Constraints: AllConstraints;
   Variables: AllVariables;
   Type: Automatic;

Objective specifies which variable is the objective function of the math program. Direction specifies whether you want to minimize or maximize the objective function. The default options AllConstraints and AllVariables apply all the declared constraints and variables in your model in the math program. Type specifies what kind of a problem the math program is, e.g., a linear program, an integer program, and so on. The default option Automatic suffices in most cases.

One feature of AIMMS is that you can have multiple mathematical programs in the same project. An example use case is a sequential goal programming problem where the solution of the first problem is provided as input to the second problem. Some of the constraints (variables) might only be applicable to one of the math programs. The default value AllConstraints (AllVariables) will apply all the constraints (variables) to all the math programs in your project. This article will show you how to model your project so that you can control the constraints (variables) imposed on a math program.

Default Constraints and Variables

When you solve a mathematical program (or generate it via the GMP functions), AIMMS will use the values of the Constraints and Variables attributes of the mathematical program identifier to determine which symbolic variables and constraints should actually be considered in the model. The default values of Constraints and Variables attributes are the predefined sets AllConstraints and AllVariables respectively. AllConstraints contains all the constraints declared in your AIMMS project and similarly, AllVariables contains all the variables.

Variables with definition

For variables with a definition, AIMMS will actually generate both the variable and an additional equality constraint. For example, if you have the variable X that has Y + Z in its definition attribute:

Variable X {
   Range: free;
   Definition: Y+Z;

AIMMS will actually generate two things:

  1. Variable X
  2. Equality constraint X_definition as X = Y + Z

So, any variable with a definition (like X) will appear in both the predeclared sets AllConstraints and AllVariables.

Selecting Constraints (Variables)

To select the constraints (variables) to be applied in a math program, you can create a set as a subset of AllConstraints (AllVariables) and use that set in the declaration of the math program instead of AllConstraints (AllVariables). The below below example shows two sets ModelConstraints and ModelVariables being used in the math program Sample_Math_Program.

You can either manually select the constraints and variables to be included in these subsets or use the definition like below to include all the constraints and variables present in a particular section or declaration section. Using a definition is recommended as it offers scalability - any new constraint or variable added inside that section will be automatically added to the subset and thereby used in the math program generation. You also do not need to worry about selecting variables with a definition in both the subsets.

Set ModelConstraints {
   SubsetOf: AllConstraints;
   Definition: AllConstraints*Section_or_Declaration_to_Optimize;

Set ModelVariables {
   SubsetOf: AllVariables;
   Definition: AllVariables*Section_or_Declaration_to_Optimize;

MathematicalProgram Sample_Math_Program {
   Objective: ObjFunc;
   Direction: maximize;
   Constraints: ModelConstraints;
   Variables: ModelVariables;
   Type: Automatic;

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Last Updated: March, 2019