The SOLVE Statement

The SOLVE statement

With the SOLVE statement you can instruct AIMMS to compute the solution of a MathematicalProgram, resulting in the following actions.

  • AIMMS determines which solution method(s) are appropriate, and checks whether the specified type is also appropriate.

  • AIMMS then generates the Jacobian matrix (first derivatives of all the constraints), the bounds on all variables and constraints, and an objective where appropriate.

  • AIMMS communicates the problem to an underlying solver that is able to perform the chosen solution method.

  • AIMMS finally reads the computed solution back from the solver.

Syntax

In addition to initiating the solution process of a MathematicalProgram, you can also use the SOLVE statement to provide local overrides of particular AIMMS settings that influence the way in which the solution process takes place. The syntax of the SOLVE statement follows.

solve-statement:

image/svg+xmlSOLVE identifier IN REPLACE MERGE MODE WHERE option := expression , ;

Replace and merge mode

You can instruct AIMMS to read back the solution in either replace or merge mode. If you do not specify a mode, AIMMS assumes replace mode. In replace mode AIMMS will, before reading back the solution of the mathematical program, remove the values of the variables in the Variables set of the mathematical program for all index tuples except those that are fixed

  • because they are not within their current domain (i.e. inactive),

  • through the NonvarStatus attribute or the .NonVar suffix of the variable,

  • because they are outside the planning interval of a Horizon (see Horizons), or

  • because their upper and lower bounds are equal.

In merge mode AIMMS will only replace the individual variable values involved in the mathematical program. This mode is very useful, for instance, when you are iteratively solving subproblems which correspond to slices of the symbolic variables in your model.

Infeasible and unbounded problems

Whenever the invoked solver finds that a mathematical program is infeasible or unbounded, AIMMS will assign one of the special values na, inf or -inf to the objective variable. For you, this will serve as a reminder of the fact that there is a problem even when you do not check the ProgramStatus and SolverStatus suffices. For all other variables, AIMMS will read back the last values computed by the solver just before returning with infeasibility or unboundedness.

Temporary option settings

Sometimes you may need some temporary option settings during a single SOLVE statement. Instead of having to change the relevant options using the OPTION statement and set them back afterwards, AIMMS also allows you to specify values for options that are used only during the current SOLVE statement. The syntax is similar to that of the OPTION statement.

Also for attributes

Apart from specifying temporary option settings you can also use the WHERE clause to override the type and direction attributes specified in the declaration of the mathematical program, as well as the solver to use for the solution process.

Example

The following SOLVE statement selects 'cplex' as its solver, sets the model type to 'rmip', and sets the CPLEX option LpMethod to 'Barrier'.

solve TransportModel in replace mode
    where solver    := 'cplex',
          type      := 'rmip',
          LpMethod  := 'Barrier' ;