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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/* */
/* This file is part of the program and library */
/* SCIP --- Solving Constraint Integer Programs */
/* */
/* Copyright 2002-2022 Zuse Institute Berlin */
/* */
/* Licensed under the Apache License, Version 2.0 (the "License"); */
/* you may not use this file except in compliance with the License. */
/* You may obtain a copy of the License at */
/* */
/* http://www.apache.org/licenses/LICENSE-2.0 */
/* */
/* Unless required by applicable law or agreed to in writing, software */
/* distributed under the License is distributed on an "AS IS" BASIS, */
/* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */
/* See the License for the specific language governing permissions and */
/* limitations under the License. */
/* */
/* You should have received a copy of the Apache-2.0 license */
/* along with SCIP; see the file LICENSE. If not visit scipopt.org. */
/* */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/**@file benderscut_int.h
* @ingroup BENDERSCUTS
* @brief Generates a Laporte and Louveaux Benders' decomposition integer cut
* @author Stephen J. Maher
*
* The classical Benders' decomposition algorithm is only applicable to problems with continuous second stage variables.
* Laporte and Louveaux (1993) developed a method for generating cuts when Benders' decomposition is applied to problem
* with discrete second stage variables. However, these cuts are only applicable when the master problem is a pure
* binary problem.
*
* The integer optimality cuts are a point-wise underestimator of the optimal subproblem objective function value.
* Similar to benderscuts_opt.c, an auxiliary variable, \f$\varphi\f$. is required in the master problem as a lower
* bound on the optimal objective function value for the Benders' decomposition subproblem.
*
* Consider the Benders' decomposition subproblem that takes the master problem solution \f$\bar{x}\f$ as input:
* \f[
* z(\bar{x}) = \min\{d^{T}y : Ty \geq h - H\bar{x}, y \mbox{ integer}\}
* \f]
* If the subproblem is feasible, and \f$z(\bar{x}) > \varphi\f$ (indicating that the current underestimators are not
* optimal) then the Benders' decomposition integer optimality cut can be generated from the optimal solution of the
* subproblem. Let \f$S_{r}\f$ be the set of indicies for master problem variables that are 1 in \f$\bar{x}\f$ and
* \f$L\f$ a known lowerbound on the subproblem objective function value.
*
* The resulting cut is:
* \f[
* \varphi \geq (z(\bar{x}) - L)(\sum_{i \in S_{r}}(x_{i} - 1) + \sum_{i \notin S_{r}}x_{i} + 1)
* \f]
*
* Laporte, G. & Louveaux, F. V. The integer L-shaped method for stochastic integer programs with complete recourse
* Operations Research Letters, 1993, 13, 133-142
*/
/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
#ifndef __SCIP_BENDERSCUT_INT_H__
#define __SCIP_BENDERSCUT_INT_H__
#include "scip/def.h"
#include "scip/type_benders.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"
#ifdef __cplusplus
extern "C" {
#endif
/** creates the integer optimality cut for Benders' decomposition cut and includes it in SCIP
*
* @ingroup BenderscutIncludes
*/
SCIP_EXPORT
SCIP_RETCODE SCIPincludeBenderscutInt(
SCIP* scip, /**< SCIP data structure */
SCIP_BENDERS* benders /**< Benders' decomposition */
);
#ifdef __cplusplus
}
#endif
#endif