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 prop_obbt.h 26 * @ingroup PROPAGATORS 27 * @brief optimization-based bound tightening propagator 28 * @author Stefan Weltge 29 * 30 * In Optimization-Based Bound Tightening (OBBT), we solve auxiliary LPs of the form 31 * \f[ 32 * \min / \max \, \{ x_i \mid x \in P' \}, 33 * \f] 34 * where \f$P'\f$ is the current LP relaxation restricted by the primal cutoff constraint \f$c^T x <= z\f$, \f$z\f$ the 35 * current cutoff bound. Trivially, the optimal objective value of this LP provides a valid lower/upper bound on 36 * variable \f$x_i\f$. 37 * 38 * Since solving LPs may be expensive, the propagator inspects solutions \f$x \in P'\f$ and does not run for variable 39 * bounds which are tight at \f$x\f$: First, we check SCIP's last LP relaxation solution. Second, we solve a sequence of 40 * filtering LP's \f$\min / \max \, \{ \sum w_i \, x_i \mid x \in P' \}\f$ in order to push several variables towards 41 * one of their bounds in one LP solve. Third, we inspect all solutions of the auxiliary LPs solved along the way. 42 * 43 * By default, OBBT is only applied for nonbinary variables that occur in nonlinear constraints. 44 * 45 * After we learned a better variable bound the propagator tries to separate the solution of the current OBBT LP with 46 * the refined outer approximation in order to strengthen the learned bound. Additionally, we trigger a 47 * propagation round of SCIP after a fixed number of learned bound tightenings. 48 * 49 * Additionally, the propagator uses the dual solution of the auxiliary LPs to construct globally valid generalized 50 * variable bounds which may be propagated during the branch-and-bound search. 51 */ 52 53 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/ 54 55 #ifndef __SCIP_PROP_OBBT_H__ 56 #define __SCIP_PROP_OBBT_H__ 57 58 #include "scip/def.h" 59 #include "scip/type_retcode.h" 60 #include "scip/type_scip.h" 61 62 #ifdef __cplusplus 63 extern "C" { 64 #endif 65 66 /** creates the obbt propagator and includes it in SCIP 67 * 68 * @ingroup PropagatorIncludes 69 */ 70 SCIP_EXPORT 71 SCIP_RETCODE SCIPincludePropObbt( 72 SCIP* scip /**< SCIP data structure */ 73 ); 74 75 #ifdef __cplusplus 76 } 77 #endif 78 79 #endif 80