Scippy

SCIP

Solving Constraint Integer Programs

benderscut_nogood.h
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4 /* SCIP --- Solving Constraint Integer Programs */
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24 
25 /**@file benderscut_nogood.h
26  * @ingroup BENDERSCUTS
27  * @brief Generates a no-good cut for solutions that are integer infeasible
28  * @author Stephen J. Maher
29  *
30  * The no-good cut is generated for the Benders' decomposition master problem if an integer solution is identified as
31  * infeasible in at least one CIP subproblems. The no-good cut is required, because the classical Benders' decomposition
32  * feasibility cuts (see benderscut_feas.c) will only cut off the solution \f$\bar{x}\f$ if the LP relaxation of the CIP
33  * is infeasible.
34  *
35  * Consider a Benders' decomposition subproblem that is a CIP and it infeasible. Let \f$S_{r}\f$ be the set of indices
36  * for master problem variables that are 1 in \f$\bar{x}\f$. The no-good cut is given by
37  *
38  * \f[
39  * 1 \leq \sum_{i \in S_{r}}(1 - x_{i}) + \sum_{i \notin S_{r}}x_{i}
40  * \f]
41  */
42 
43 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
44 
45 #ifndef __SCIP_BENDERSCUT_NOGOOD_H__
46 #define __SCIP_BENDERSCUT_NOGOOD_H__
47 
48 
49 #include "scip/def.h"
50 #include "scip/type_benders.h"
51 #include "scip/type_retcode.h"
52 #include "scip/type_scip.h"
53 
54 #ifdef __cplusplus
55 extern "C" {
56 #endif
57 
58 /** creates the no good Benders' decomposition cut and includes it in SCIP
59  *
60  * @ingroup BenderscutIncludes
61  */
62 SCIP_EXPORT
64  SCIP* scip, /**< SCIP data structure */
65  SCIP_BENDERS* benders /**< Benders' decomposition */
66  );
67 
68 #ifdef __cplusplus
69 }
70 #endif
71 
72 #endif
SCIP_RETCODE SCIPincludeBenderscutNogood(SCIP *scip, SCIP_BENDERS *benders)
enum SCIP_Retcode SCIP_RETCODE
Definition: type_retcode.h:63
type definitions for return codes for SCIP methods
type definitions for SCIP&#39;s main datastructure
type definitions for Benders&#39; decomposition methods
common defines and data types used in all packages of SCIP