## Detailed Description

type definitions for Benders' decomposition methods

Definition in file type_benders.h.

Go to the source code of this file.

## Typedefs | |

typedef enum SCIP_BendersEnfoType | SCIP_BENDERSENFOTYPE |

typedef enum SCIP_BendersSolveLoop | SCIP_BENDERSSOLVELOOP |

typedef enum SCIP_BendersSubStatus | SCIP_BENDERSSUBSTATUS |

typedef enum SCIP_BendersSubType | SCIP_BENDERSSUBTYPE |

typedef struct SCIP_Benders | SCIP_BENDERS |

typedef struct SCIP_BendersData | SCIP_BENDERSDATA |

typedef struct SCIP_SubproblemSolveStat | SCIP_SUBPROBLEMSOLVESTAT |

## Enumerations | |

enum | SCIP_BendersEnfoType { SCIP_BENDERSENFOTYPE_LP = 1, SCIP_BENDERSENFOTYPE_RELAX = 2, SCIP_BENDERSENFOTYPE_PSEUDO = 3, SCIP_BENDERSENFOTYPE_CHECK = 4 } |

enum | SCIP_BendersSolveLoop { SCIP_BENDERSSOLVELOOP_CONVEX = 0, SCIP_BENDERSSOLVELOOP_CIP = 1, SCIP_BENDERSSOLVELOOP_USERCONVEX = 2, SCIP_BENDERSSOLVELOOP_USERCIP = 3 } |

enum | SCIP_BendersSubStatus { SCIP_BENDERSSUBSTATUS_UNKNOWN = 0, SCIP_BENDERSSUBSTATUS_OPTIMAL = 1, SCIP_BENDERSSUBSTATUS_AUXVIOL = 2, SCIP_BENDERSSUBSTATUS_INFEAS = 3 } |

enum | SCIP_BendersSubType { SCIP_BENDERSSUBTYPE_CONVEXCONT = 0, SCIP_BENDERSSUBTYPE_CONVEXDIS = 1, SCIP_BENDERSSUBTYPE_NONCONVEXCONT = 2, SCIP_BENDERSSUBTYPE_NONCONVEXDIS = 3, SCIP_BENDERSSUBTYPE_UNKNOWN = 4 } |

## Macro Definition Documentation

## ◆ SCIP_DECL_BENDERSCOPY

#define SCIP_DECL_BENDERSCOPY | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders, SCIP_Bool threadsafe) |

copy method for Benders' decomposition plugins (called when SCIP copies plugins). If there is an active Benders' decomposition, all copies are not valid. As such, there is no valid parameter that is passed to the callback function

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself
- threadsafe : must the Benders' decomposition copy be thread safe

Definition at line 95 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSFREE

#define SCIP_DECL_BENDERSFREE | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

destructor of Benders' decomposition to free user data (called when SCIP is exiting)

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 103 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSINIT

#define SCIP_DECL_BENDERSINIT | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

initialization method of Benders' decomposition (called after problem was transformed and the Benders' decomposition is active)

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 112 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSEXIT

#define SCIP_DECL_BENDERSEXIT | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

deinitialization method of Benders' decomposition (called before transformed problem is freed and the Benders' decomposition is active)

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 121 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSINITPRE

#define SCIP_DECL_BENDERSINITPRE | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

presolving initialization method of the Benders' decomposition (called when presolving is about to begin)

This function is called immediately after the auxiliary variables are created in the master problem. The callback provides the user an opportunity to add variable data to the auxiliary variables.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 132 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSEXITPRE

#define SCIP_DECL_BENDERSEXITPRE | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

presolving deinitialization method of the Benders' decomposition (called after presolving has been finished)

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 140 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSINITSOL

#define SCIP_DECL_BENDERSINITSOL | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

solving process initialization method of Benders' decomposition (called when branch and bound process is about to begin)

This method is called when the presolving was finished and the branch and bound process is about to begin. The Benders' decomposition may use this call to initialize its branch and bound specific data.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 151 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSEXITSOL

#define SCIP_DECL_BENDERSEXITSOL | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders) |

solving process deinitialization method of Benders' decomposition (called before branch and bound process data is freed)

This method is called before the branch and bound process is freed. The Benders' decomposition should use this call to clean up its branch and bound data.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition itself

Definition at line 162 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSCREATESUB

#define SCIP_DECL_BENDERSCREATESUB | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders, int probnumber) |

the method for creating the Benders' decomposition subproblem. This method is called during the initialisation stage (after the master problem was transformed).

- Note
- When the create subproblem callback is invoked, the mapping between the master problem and subproblem variables must be available. The create subproblem callback is invoked immediately after BENDERSINIT. So, it is possible to construct the variable mapping within the BENDERSINIT callback.

This method must register the SCIP instance for the subproblem with the Benders' decomposition core by calling SCIPaddBendersSubproblem. Typically, the user must create the SCIP instances for the subproblems. These can be created within a reader or probdata and then registered with the Benders' decomposition core during the call of this callback. If there are any settings required for solving the subproblems, then they should be set here. However, some settings will be overridden by the standard solving method included in the Benders' decomposition framework. If a special solving method is desired, the user can implement the bendersSolvesubXyz callback. In this latter case, it is possible to provide a NULL pointer to SCIPaddBendersSubproblem. This will ensure that no internal solving methods available within the Benders' decomposition core are invoked during the solving process.

If the user defines a subproblem solving method, then in BENDERSCREATESUB, the user must explicitly specify the subproblem type. This is necessary because the dual solutions from convex problems can be used to generate cuts. The classical Benders' optimality and feasibility cuts require that the subproblems are convex. The subproblem type is specified by calling SCIPbendersSetSubproblemType. The available subproblem types are defined in SCIP_BENDERSSUBTYPE.

If the user does NOT implement a subproblem solving method, then the convexity of the problem is determined internally.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition data structure
- probnumber : the subproblem problem number

Definition at line 194 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSPRESUBSOLVE

#define SCIP_DECL_BENDERSPRESUBSOLVE | ( | x | ) |

**Value:**

**Definition:**struct_scip.h:68

**Definition:**struct_benders.h:57

**Definition:**struct_sol.h:73

**Definition:**objbenders.h:43

called before the subproblem solving loop for Benders' decomposition. The pre subproblem solve function gives the user an oppportunity to perform any global set up for the Benders' decomposition.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition data structure
- sol : the solution that will be checked in the subproblem. Can be NULL.
- type : the enforcement type that called the Benders' decomposition solve.
- checkint : should the integer subproblems be checked.
- infeasible : flag to return whether the master problem in infeasible with respect to the added cuts
- auxviol : set to TRUE only if the solution is feasible but the aux vars are violated
- skipsolve : flag to return whether the current subproblem solving loop should be skipped
- result : a result to be returned to the Benders' constraint handler if the solve is skipped. If the solve is not skipped, then the returned result is ignored.

possible return values for *result (if more than one applies, the first in the list should be used):

- SCIP_DIDNOTRUN : the subproblem was not solved in this iteration. Other decompositions will be checked.
- SCIP_CONSADDED : a constraint has been added to the master problem. No other decompositions will be checked.
- SCIP_SEPARATED : a cut has been added to the master problem. No other decompositions will be checked.
- SCIP_FEASIBLE : feasibility of the solution is reported to SCIP. Other decompositions will be checked.
- SCIP_INFEASIBLE : infeasibility of the solution is reported to SCIP. No other decompositions will be checked.

Definition at line 218 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSSOLVESUBCONVEX

#define SCIP_DECL_BENDERSSOLVESUBCONVEX | ( | x | ) |

**Value:**

**Definition:**struct_scip.h:68

**Definition:**struct_benders.h:57

**Definition:**struct_sol.h:73

**Definition:**objbenders.h:43

the solving method for a convex Benders' decomposition subproblem. This call back is provided to solve problems for which the dual soluitons are used to generate Benders' decomposition cuts. In the classical Benders' decomposition implementation, this would be an LP. However, it can be any convex problem where the dual solutions are given by a single vector of reals.

In the Benders' decomposition subproblem solving process, there are two solving loops. The first is where the convex subproblems, and the convex relaxations of subproblems, are solved. If no cuts are generated after this solving loop, then the second loop solves subproblems defined as CIPs. This callback is executed during the FIRST solving loop only.

In the classical Benders' decomposition implementation, if the subproblems are all LPs the only the BENDERSSOLVESUBCONVEX need to be implemented. If the subproblems are MIPs, then it is useful to only implement a single SCIP instance for the subproblem and then change the variable types of the appropriate variables to CONTINUOUS for the CONVEX subproblem solve and to INTEGER for the CIP subproblem solve.

The solving methods are separated so that they can be called in parallel.

NOTE: The solving methods must be thread safe.

This method is called from within the execution method.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition data structure
- sol : the solution that will be checked in the subproblem. Can be NULL.
- probnumber : the subproblem problem number
- onlyconvexcheck : flag to indicate that only the convex relaxations will be checked in this solving loop. This is a feature of the Large Neighbourhood Benders' Search
- objective : variable to return the objective function value of the subproblem
- result : the result from solving the subproblem

possible return values for *result (if more than one applies, the first in the list should be used):

- SCIP_DIDNOTRUN : the subproblem was not solved in this iteration
- SCIP_FEASIBLE : the subproblem is solved and is feasible
- SCIP_INFEASIBLE : the subproblem is solved and is infeasible
- SCIP_UNBOUNDED : the subproblem is solved and is unbounded

Definition at line 259 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSSOLVESUB

#define SCIP_DECL_BENDERSSOLVESUB | ( | x | ) |

**Value:**

**Definition:**struct_scip.h:68

**Definition:**struct_benders.h:57

**Definition:**struct_sol.h:73

**Definition:**objbenders.h:43

the solving method for a Benders' decomposition subproblem as a CIP. This call back is provided to solve problems for which the dual solutions are not well defined. In this case, the cuts are typically generated from the primal solution to the CIP. In the classical Benders' decomposition implementation, this would be a MIP. However, it can be any CIP.

In the Benders' decomposition subproblem solving process, there are two solving loops. The first is where the convex subproblems, and the convex relaxations of subproblems, are solved. If no cuts are generated after this solving loop, then the second loop solves subproblems defined as CIPs. This callback is executed during the SECOND solving loop only.

The solving methods are separated so that they can be called in parallel.

NOTE: The solving methods must be thread safe.

This method is called from within the execution method.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition data structure
- sol : the solution that will be checked in the subproblem. Can be NULL.
- probnumber : the subproblem problem number
- objective : variable to return the objective function value of the subproblem
- result : the result from solving the subproblem

possible return values for *result (if more than one applies, the first in the list should be used):

- SCIP_DIDNOTRUN : the subproblem was not solved in this iteration
- SCIP_FEASIBLE : the subproblem is solved and is feasible
- SCIP_INFEASIBLE : the subproblem is solved and is infeasible
- SCIP_UNBOUNDED : the subproblem is solved and is unbounded

Definition at line 292 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSPOSTSOLVE

#define SCIP_DECL_BENDERSPOSTSOLVE | ( | x | ) |

**Value:**

**Definition:**struct_scip.h:68

**Definition:**struct_benders.h:57

**Definition:**struct_sol.h:73

**Definition:**objbenders.h:43

the post-solve method for Benders' decomposition. The post-solve method is called after the subproblems have been solved but before they have been freed. After the solving of the Benders' decomposition subproblems, the subproblem solving data is freed in the SCIP_DECL_BENDERSFREESUB callback. However, it is not necessary to implement SCIP_DECL_BENDERSFREESUB.

If SCIP_DECL_BENDERSFREESUB is not implemented, then the Benders' decomposition framework will perform a default freeing of the subproblems. If a subproblem is an LP, then they will be in probing mode for the subproblem solve. So the freeing process involves ending the probing mode. If the subproblem is a MIP, then the subproblem is solved by calling SCIPsolve. As such, the transformed problem must be freed after each subproblem solve.

This callback provides the opportunity for the user to clean up any data structures that should not exist beyond the current iteration. The user has full access to the master and subproblems in this callback. So it is possible to construct solution for the master problem in the method. Additionally, if there are any subproblems that are infeasibility and this can not be resolved, then the it is possible to merge these subproblems into the master problem. The subproblem indices are given in the mergecands array. The merging can be perform by a user defined function or by calling SCIPmergeBendersSubproblemIntoMaster. If a subproblem was merged into the master problem, then the merged flag must be set to TRUE.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition data structure
- sol : the solution that was checked by solving the subproblems. Can be NULL.
- type : the enforcement type that called the Benders' decomposition solve.
- mergecands : the subproblems that are candidates for merging into the master problem, the first npriomergecands are the priority candidates (they should be merged). The remaining (nmergecands - npriomergecands) are subproblems that could be merged if desired.
- npriomergecands : the number of priority merge candidates.
- nmergecands : the total number of subproblems that are candidates for merging into the master problem
- checkint : should the integer subproblems be checked.
- infeasible : indicates whether at least one subproblem is infeasible
- merged : flag to indicate whether a subproblem was merged into the master problem.

Definition at line 328 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSFREESUB

#define SCIP_DECL_BENDERSFREESUB | ( | x | ) | SCIP_RETCODE x (SCIP* scip, SCIP_BENDERS* benders, int probnumber) |

frees the subproblem so that it can be resolved in the next iteration. As stated above, it is not necessary to implement this callback. If the callback is implemented, the subproblems should be freed by calling SCIPfreeTransform(). However, if the subproblems are LPs, then it could be more efficient to put the subproblem into probing mode prior to solving and then exiting the probing mode during the callback. To put the subproblem into probing mode, the subproblem must be in SCIP_STAGE_SOLVING. This can be achieved by using eventhandlers.

If SCIP_DECL_BENDERSFREESUB is not implemented, then the Benders' decomposition framework will perform a default freeing of the subproblems. If a subproblem is an LP, then they will be in probing mode for the subproblem solve. So the freeing process involves ending the probing mode. If the subproblem is a MIP, then the subproblem is solved by calling SCIPsolve. As such, the transformed problem must be freed after each subproblem solve.

NOTE: The freeing methods must be thread safe.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition data structure
- probnumber : the subproblem problem number

Definition at line 350 of file type_benders.h.

## ◆ SCIP_DECL_BENDERSGETVAR

#define SCIP_DECL_BENDERSGETVAR | ( | x | ) |

**Value:**

**Definition:**struct_scip.h:68

**Definition:**struct_var.h:207

**Definition:**struct_benders.h:57

**Definition:**objbenders.h:43

the variable mapping from the subproblem to the master problem. It is neccessary to have a mapping between every master problem variable and its counterpart in the subproblem. This mapping must go both ways: from master to sub and sub to master.

This method is called when generating the cuts. The cuts are generated by using the solution to the subproblem to eliminate a solution to the master problem.

input:

- scip : SCIP main data structure
- benders : the Benders' decomposition structure
- var : the variable for which the corresponding variable in the master or subproblem is required
- mappedvar : pointer to store the variable that is mapped to var
- probnumber : the number of the subproblem that the desired variable belongs to, -1 for the master problem

Definition at line 366 of file type_benders.h.

## Typedef Documentation

## ◆ SCIP_BENDERSENFOTYPE

typedef enum SCIP_BendersEnfoType SCIP_BENDERSENFOTYPE |

indicates the callback in cons_benders and cons_benderslp that triggered the subproblem solve

Definition at line 51 of file type_benders.h.

## ◆ SCIP_BENDERSSOLVELOOP

typedef enum SCIP_BendersSolveLoop SCIP_BENDERSSOLVELOOP |

identifies the type of problem solved in each solve loop

Definition at line 60 of file type_benders.h.

## ◆ SCIP_BENDERSSUBSTATUS

typedef enum SCIP_BendersSubStatus SCIP_BENDERSSUBSTATUS |

Definition at line 69 of file type_benders.h.

## ◆ SCIP_BENDERSSUBTYPE

typedef enum SCIP_BendersSubType SCIP_BENDERSSUBTYPE |

Definition at line 79 of file type_benders.h.

## ◆ SCIP_BENDERS

typedef struct SCIP_Benders SCIP_BENDERS |

Benders' decomposition data

Definition at line 81 of file type_benders.h.

## ◆ SCIP_BENDERSDATA

typedef struct SCIP_BendersData SCIP_BENDERSDATA |

locally defined Benders' decomposition data

Definition at line 82 of file type_benders.h.

## ◆ SCIP_SUBPROBLEMSOLVESTAT

typedef struct SCIP_SubproblemSolveStat SCIP_SUBPROBLEMSOLVESTAT |

the solving statistics of the subproblems

Definition at line 83 of file type_benders.h.

## Enumeration Type Documentation

## ◆ SCIP_BendersEnfoType

enum SCIP_BendersEnfoType |

Definition at line 44 of file type_benders.h.

## ◆ SCIP_BendersSolveLoop

Definition at line 53 of file type_benders.h.

## ◆ SCIP_BendersSubStatus

Definition at line 62 of file type_benders.h.

## ◆ SCIP_BendersSubType

enum SCIP_BendersSubType |

Definition at line 71 of file type_benders.h.