# Adapt Solve Procedure with Callbacks for GMP¶

This article presents a general guide to converting from `solve`

statements to using GMP, and how to adapt the existing callbacks and their activation.

As an experienced model builder, you may want to convert from solving using the `solve`

statement to using GMP functionality (with prefix `gmp::`

). Using GMP offers several benefits, such as:

Speed up Monte Carlo analysis

Work with multiple solutions

Use multi-objective, both weighted and lexicographic

Solve in parallel

However, when callbacks are used on the mathematical program, the callback procedures need to be modified and activated differently when using GMP.

## Original solve procedure¶

We have a flow shop model that is solved by the following procedure `pr_DoSolve`

with body:

1 2 3 4 5 6 7 8 | ```
Empty AllVariables;
pr_GenerateData();
empty s_Timepoints ;
FlowShopModel.CallbackTime := 'pr_TimeCallback'; ! Solve style callback.
block where progress_time_interval := 1 ;
solve FlowShopModel;
endblock ;
pr_prepInterface;
``` |

On line 4 a callback is activated for the flowshop model by setting the corresponding suffix for the mathematical program.

The callback procedure itself is:

1 2 3 4 5 | ```
Procedure pr_TimeCallback {
Body: {
pr_updateGap(FlowShopModel.bestbound, FlowShopModel.Incumbent);
}
}
``` |

As you can see, it uses the suffixes `.bestbound`

and `.Incumbent`

which are set before this procedure is invoked.

An example solve results in the following progress window:

As you can see, optimality is reached.

Example Project 1

If you want to replay this yourself, please download and run `1.flowshop...zip`

and press the solve button in the lower right corner.

## Declaring the GMP¶

The Generated Mathematical Programs are objects stored in AIMMS internally. Each object is given an identification as an element in the predeclared set `AllGeneratedMathematicalPrograms`

. We use an element parameter to store such an element after generating, so that we can reference it in later manipulations such as solving. The declaration is:

1 2 3 | ```
ElementParameter ep_GMP {
Range: AllGeneratedMathematicalPrograms;
}
``` |

With this declaration, we can simply convert.

1 2 3 4 5 6 7 8 9 | ```
Empty AllVariables;
pr_GenerateData();
empty s_Timepoints ;
FlowShopModel.CallbackTime := 'pr_TimeCallback'; ! Solve style callback.
block where progress_time_interval := 1 ;
ep_GMP := gmp::Instance::Generate( FlowShopModel );
gmp::Instance::Solve( ep_GMP );
endblock ;
pr_prepInterface;
``` |

The only difference in coding the solution procedure is then on lines 6 and 7, highlighted above. Running that procedure gives the unexpected result:

As you can see, optimality is not reached; instead you’ll get the following warning:

```
After zero iterations CPLEX 12.9 found an integer solution to FlowShopModel. The minimum found for TimeSpan is 1865.
```

This is caused by the different interface for callbacks. We will handle that in the next section.

Example Project 2

If you want to replay this yourself, please download and run `2.flowshop...zip`

and press the solve button in the lower right corner.

## Adapting callbacks for GMP¶

GMP style callback procedures have the input argument `ep_session`

which is an element parameter in the set `AllSolverSessions`

. This gives you access to solver session specific information. The return value of the callback procedure should be `0`

to stop solving, or `1`

to continue solving.

The best practice is to have an explicit return statement as the last statement of a callback procedure. This results in the following replacement of the `pr_TimeCallback`

procedure.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
Procedure pr_TimeCallback {
Arguments: (ep_session);
Body: {
p_BestBound := GMP::SolverSession::GetBestBound( ep_session );
pr_updateGap(p_BestBound, p_BestIncumbent);
return 1 ; ! Indicate to the solver to continue.
}
ElementParameter ep_session {
Range: AllSolverSessions;
Property: Input;
}
Parameter p_BestBound;
}
``` |

The solver session allows you to obtain various information from the session directly, but not the incumbent. Instead, we register the latest incumbent value ourselves when the solver finds a new incumbent solution. This requires the following additional procedure:

1 2 3 4 5 6 7 8 9 10 11 12 | ```
Procedure pr_IncumbentCallback {
Arguments: (ep_session);
Body: {
p_BestIncumbent := GMP::SolverSession::GetObjective( ep_session );
return 1 ; ! Indicate to the solver to continue.
}
ElementParameter ep_session {
Range: AllSolverSessions;
Property: Input;
}
}
``` |

These two callback routines are activated as shown in the following version of the procedure `pr_DoSolve`

:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
Empty AllVariables;
pr_GenerateData();
p_BestIncumbent := 1000;
empty s_Timepoints ;
block where progress_time_interval := 1 ;
ep_GMP := gmp::Instance::Generate( FlowShopModel );
gmp::Instance::SetCallbackTime(
GMP : ep_GMP,
callback : 'pr_TimeCallback');
GMP::Instance::SetCallbackNewIncumbent(
GMP : ep_GMP,
callback : 'pr_IncumbentCallback');
gmp::Instance::Solve( ep_GMP );
endblock ;
pr_prepInterface;
``` |

After running the adapted model, the progress window shows the following results:

Example Project 3

If you want to replay this yourself, please download and run `3.flowshop...zip`

and press the solve button in the lower right corner.

You have now converted the Solve statement to use GMP!

Last Updated: September, 2020