Pricing problem solvers are called by the pricer to solve a single pricing problem either heuristically or to optimality and return a set of solutions.

A complete list of all pricing problem solvers contained in this release can be found here.

In the following, we explain how the user can add his own pricing problem solver. Take the generic MIP pricing problem solver (src/solver_mip.c) as an example. As all other default plug-ins, it is written in C. There is currently no C++ wrapper available.

Additional documentation for the callback methods of pricing problem solvers, in particular for their input parameters, can be found in the file type_solver.h.

Here is what you have to do to implement a pricing problem solver:

- Copy the template files src/solver_xyz.c and src/solver_xyz.h into files named "solver_mysolver.c" and "solver_mysolver.h".

Make sure to adjust your Makefile such that these files are compiled and linked to your project. - Open the new files with a text editor and replace all occurrences of "xyz" by "mysolver".
- Adjust the properties of the solver (see Properties of a pricing problem solver).
- Define the solver data (see Solver Data). This is optional.
- Implement the interface methods (see Interface Methods).
- Implement the fundamental callback methods (see Fundamental Callback Methods of a Solver).
- Implement the additional callback methods (see Additional Callback Methods of a Solver). This is optional.

# Properties of a pricing problem solver

At the top of the new file "solver_mysolver.c", you can find the solver properties. These are given as compiler defines. The properties you have to set have the following meaning:

- SOLVER_NAME: the name of the solver.
- This name is used in the interactive shell to address the solver. Names have to be unique: no two solvers may have the same name.

- SOLVER_DESC: the description of the solver.
- This string is printed as description of the solver in the interactive shell.

- SOLVER_PRIORITY: the priority of the solver.
- Whenever a pricing problem has to be solved, the solvers are called in a predefined order, until one of the solvers solved the pricing problem. This order is given by the priorities of the solvers; they are called in the order of decreasing priority.

The priority of the solver should be set according to the range of problems it can solve. The more specialized a solver is, the higher its priority should be in order to be called before more general solvers that also cover this type of problem. The default pricing solver that solves the pricing problem as a MIP using SCIP has priority 0, so all other pricing solvers should have positive priority. An easy way to list the priorities and descriptions of all solvers is "display solvers" in the interactive shell of GCG.

# Solver Data

Below the header "Data structures" you can find the struct "struct GCG_SolverData". In this data structure, you can store the data of your solver. For example, you should store the adjustable parameters of the solver in this data structure and also arrays to store the solutions that you return after solving a pricing problem (see solver_mip.c). Defining solver data is optional. You can leave this struct empty.

# Interface Methods

At the bottom of "solver_mysolver.c", you can find the interface method GCGincludeSolverMysolver(), which also appears in "solver_mysolver.h".

This method has to be adjusted only slightly. It is responsible for notifying GCG (and especially the pricer in the master SCIP instance) of the presence of the solver by calling the method GCGpricerIncludeSolver(). SCIPincludeSolverMysolver() should be called by the user, if he wants to include the solver, i.e., if he wants to use the solver in his application. This can done for example by adding

If you are using solver data, you have to allocate the memory for the data at this point. You can do this by calling

You can also initialize the fields in struct SCIP_SolverData afterwards. For freeing the solver data, see SOLVEREXIT. Alternatively, you can also initialize and free the fields in the solver data in the SOLVERINITSOL and SOLVEREXITSOL callback methods, respectively. For an example, see solver_mip.c.

You may also add user parameters for your solver, see the SCIP documentation for how to add user parameters and the method SCIPincludeSolverMip() in solver_mip.c for an example.

# Fundamental Callback Methods of a Solver

The fundamental callback methods of the plug-ins are the ones that have to be implemented in order to obtain an operational algorithm. Pricing problem solvers do not have fundamental callback methods, but they should implement at least of the SOLVERSOLVE and SOVLERSOLVEHEUR methods.

Additional documentation to the callback methods, in particular to their input parameters, can be found in type_solver.h.

# Additional Callback Methods of a Solver

## SOLVERSOLVE

The SOLVERSOLVE callback is called when the variable pricer in the master SCIP instance wants to solve a pricing problem to optimality. It is given a SCIP instance representing the pricing problem that should be solved and should check whether the pricing problem has a structure that can be handled by the solver. If so, it should solve the pricing problem to optimality and return the optimal objective value of the problem (to be stored in the lowerbound pointer) along with a set of primal feasible solutions (including the optimal one).

The solutions should be returned by setting some given pointers: solvars should store the number of solutions returned, nsolvars should point to an array storing for each solution the number of variables with non-zero value, and solisray should point to an array storing for each solution whether it represents an extreme point of the pricing problem or an extreme ray. Furthermore, solvars and solvals should point to arrays storing for each solution an array of variables and corresponding solution values, respectively (leaving out variables with value 0). Therefore, a pricing problem solver should manage these arrays in its own data structure, fill them after solving a pricing problem and set the return pointers to these arrays. Have a look at solver_mip.c for an example of how this can be done.

Last, the callback should adjust the given result pointer to SCIP_STATUS_OPTIMAL if the problem was solved to optimality, to SCIP_STATUS_UNBOUNDED if the problem was solved and is unbounded, or SCIP_STATUS_UNKNOWN if the solver was not applicable to the pricing problem or if the solving was stopped.

The given SCIP instance representing the pricing problem can be seen as a container to store all information about the pricing problem. During the solving process, especially the objective function coefficients change according to the current dual solution and branching might change bounds in the pricing problem or add constraints. If the structure of the problem is independent of the changes that can occur with the selected branching rule, the structure detection for the pricing problems can also be done in the SOLVERINITSOL callback and stored internally to avoid doing it every time a pricing problem is solved.

## SOLVERSOLVEHEUR

The SOLVERSOLVEHEUR callback is called during heuristic pricing when the variable pricer in the master SCIP instance wants to solve a pricing problem heuristically. It has the same input and return parameters as the SOLVERSOLVE callback. It does not need to solve the pricing problem to optimality, but should try to construct good feasible solutions using fast methods. Nevertheless, it can return a lower bound for the optimal solution value of the problem, if it computes one.

## SOLVERFREE

If you are using solver data, you have to implement this method in order to free the solver data. This can be done by the following procedure:

If you have allocated memory for fields in your solver data, remember to free this memory before freeing the pricing solver data itself.

## SOLVERINIT

The SOLVERINIT callback is executed after the problem is transformed. The pricing problem solver may, e.g., use this call to replace the original constraints stored in its solver data by transformed constraints, or to initialize other elements of his solver data.

## SOLVEREXIT

The SOLVEREXIT callback is executed before the transformed problem is freed. In this method the pricing problem solver should free all resources that have been allocated for the solving process in SOLVERINIT.

## SOLVERINITSOL

The SOLVERINITSOL callback is executed when the presolving is finished and the branch-and-bound process is about to begin. The pricing problem solver may use this call to initialize its branch-and-bound specific data.

## SOLVEREXITSOL

The SOLVEREXITSOL callback is executed before the branch-and-bound process is freed. The pricing problem solver should use this call to clean up its branch-and-bound data, which was allocated in SOLVERINITSOL.