heur_trustregion.h

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/**@file   heur_trustregion.h
 * @ingroup PRIMALHEURISTICS
 * @brief  Large neighborhood search heuristic for Benders' decomposition based on trust region methods
 * @author Stephen J. Maher
 *
 * The Trust Region heuristic draws upon trust region methods for solving optimization problems, especially in the
 * context of Benders' decomposition. This heuristic has been developed to improve the heuristic performance of the
 * Benders' decomposition algorithm within SCIP.
 *
 * The Trust Region heuristic copies the original SCIP instance and adds a constraint to penalize changes from the
 * incumbent solution. Consider a problem that includes a set of binary variables \f$\mathcal{B}\f$. Given a feasible
 * solution \f$\hat{x}\f$ to the original problem, we define the set \f$\mathcal{B}^{+}\f$ as the index set for the
 * binary variables that are 1 in the input solution and \f$\mathcal{B}^{-}\f$ as the index set for binary variables
 * that are 0. The trust region constraint, which is added to the sub-SCIP, is given by
 *
 * \f[
 *    \sum_{i \in \mathcal{B}^{+}}(1 - x_{i}) + \sum_{i \in \mathcal{B}^{-}}x_{i} \le \theta
 * \f]
 *
 * The variable \f$\theta\f$ measure the distance, in terms of the binary variables, of candidate solutions to the input
 * solution.
 *
 * In addition, an upper bounding constraint is explicitly added to enforce a minimum improvement from the heuristic,
 * given by \f$f(x) \le f(\hat{x}) - \epsilon\f$. The parameter \f$\epsilon \ge 0\f$ denotes the minimum improvement
 * that must be achieved by the heuristic.
 *
 * The objective function is then modified to \f$f(x) + M\theta\f$, where \f$M\f$ is a parameter for penalizing the
 * distance of solutions from the input solution \f$\hat{x}\f$.
 *
 * If a new incumbent solution is found by this heuristic, then the Trust Region heuristic is immediately
 * re-executed with this new incumbent solution.
 */
 
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#ifndef __SCIP_HEUR_TRUSTREGION_H__
#define __SCIP_HEUR_TRUSTREGION_H__
 
#include "scip/def.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
/** creates local branching primal heuristic and includes it in SCIP
 *
 *  @ingroup PrimalHeuristicIncludes
 */
SCIP_EXPORT
SCIP_RETCODE SCIPincludeHeurTrustregion(
   SCIP*                 scip                /**< SCIP data structure */
   );
 
#ifdef __cplusplus
}
#endif
 
#endif