prop_obbt.h

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/**@file    prop_obbt.h
 * @ingroup PROPAGATORS
 * @brief   optimization-based bound tightening propagator
 * @author  Stefan Weltge
 *
 * In Optimization-Based Bound Tightening (OBBT), we solve auxiliary LPs of the form
 * \f[
 *      \min / \max \, \{ x_i \mid x \in P' \},
 * \f]
 * 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
 * current cutoff bound. Trivially, the optimal objective value of this LP provides a valid lower/upper bound on
 * variable \f$x_i\f$.
 *
 * Since solving LPs may be expensive, the propagator inspects solutions \f$x \in P'\f$ and does not run for variable
 * bounds which are tight at \f$x\f$: First, we check SCIP's last LP relaxation solution. Second, we solve a sequence of
 * filtering LP's \f$\min / \max \, \{ \sum w_i \, x_i \mid x \in P' \}\f$ in order to push several variables towards
 * one of their bounds in one LP solve. Third, we inspect all solutions of the auxiliary LPs solved along the way.
 *
 * By default, OBBT is only applied for nonbinary variables that occur in nonlinear constraints.
 *
 * After we learned a better variable bound the propagator tries to separate the solution of the current OBBT LP with
 * the refined outer approximation in order to strengthen the learned bound. Additionally, we trigger a
 * propagation round of SCIP after a fixed number of learned bound tightenings.
 *
 * Additionally, the propagator uses the dual solution of the auxiliary LPs to construct globally valid generalized
 * variable bounds which may be propagated during the branch-and-bound search.
 */
 
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#ifndef __SCIP_PROP_OBBT_H__
#define __SCIP_PROP_OBBT_H__
 
#include "scip/def.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
/** creates the obbt propagator and includes it in SCIP
 *
 * @ingroup PropagatorIncludes
 */
SCIP_EXPORT
SCIP_RETCODE SCIPincludePropObbt(
   SCIP*                 scip                /**< SCIP data structure */
   );
 
#ifdef __cplusplus
}
#endif
 
#endif