1 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 2 /* */ 3 /* This file is part of the program and library */ 4 /* SCIP --- Solving Constraint Integer Programs */ 5 /* */ 6 /* Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB) */ 7 /* */ 8 /* Licensed under the Apache License, Version 2.0 (the "License"); */ 9 /* you may not use this file except in compliance with the License. */ 10 /* You may obtain a copy of the License at */ 11 /* */ 12 /* http://www.apache.org/licenses/LICENSE-2.0 */ 13 /* */ 14 /* Unless required by applicable law or agreed to in writing, software */ 15 /* distributed under the License is distributed on an "AS IS" BASIS, */ 16 /* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */ 17 /* See the License for the specific language governing permissions and */ 18 /* limitations under the License. */ 19 /* */ 20 /* You should have received a copy of the Apache-2.0 license */ 21 /* along with SCIP; see the file LICENSE. If not visit scipopt.org. */ 22 /* */ 23 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 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 63 SCIP_RETCODE SCIPincludeBenderscutNogood( 64 SCIP* scip, /**< SCIP data structure */ 65 SCIP_BENDERS* benders /**< Benders' decomposition */ 66 ); 67 68 #ifdef __cplusplus 69 } 70 #endif 71 72 #endif 73