Scippy

SCIP

Solving Constraint Integer Programs

prop_obbt.h
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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) */
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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
72  SCIP* scip /**< SCIP data structure */
73  );
74 
75 #ifdef __cplusplus
76 }
77 #endif
78 
79 #endif
SCIP_RETCODE SCIPincludePropObbt(SCIP *scip)
Definition: prop_obbt.c:3158
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
common defines and data types used in all packages of SCIP