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2    	/*                                                                           */
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4    	/*         SCIP --- Solving Constraint Integer Programs                      */
5    	/*                                                                           */
6    	/*  Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB)                      */
7    	/*                                                                           */
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19   	/*                                                                           */
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22   	/*                                                                           */
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24   	
25   	/**@file   heur_trustregion.h
26   	 * @ingroup PRIMALHEURISTICS
27   	 * @brief  Large neighborhood search heuristic for Benders' decomposition based on trust region methods
28   	 * @author Stephen J. Maher
29   	 *
30   	 * The Trust Region heuristic draws upon trust region methods for solving optimization problems, especially in the
31   	 * context of Benders' decomposition. This heuristic has been developed to improve the heuristic performance of the
32   	 * Benders' decomposition algorithm within SCIP.
33   	 *
34   	 * The Trust Region heuristic copies the original SCIP instance and adds a constraint to penalize changes from the
35   	 * incumbent solution. Consider a problem that includes a set of binary variables \f$\mathcal{B}\f$. Given a feasible
36   	 * solution \f$\hat{x}\f$ to the original problem, we define the set \f$\mathcal{B}^{+}\f$ as the index set for the
37   	 * binary variables that are 1 in the input solution and \f$\mathcal{B}^{-}\f$ as the index set for binary variables
38   	 * that are 0. The trust region constraint, which is added to the sub-SCIP, is given by
39   	 *
40   	 * \f[
41   	 *    \sum_{i \in \mathcal{B}^{+}}(1 - x_{i}) + \sum_{i \in \mathcal{B}^{-}}x_{i} \le \theta
42   	 * \f]
43   	 *
44   	 * The variable \f$\theta\f$ measure the distance, in terms of the binary variables, of candidate solutions to the input
45   	 * solution.
46   	 *
47   	 * In addition, an upper bounding constraint is explicitly added to enforce a minimum improvement from the heuristic,
48   	 * given by \f$f(x) \le f(\hat{x}) - \epsilon\f$. The parameter \f$\epsilon \ge 0\f$ denotes the minimum improvement
49   	 * that must be achieved by the heuristic.
50   	 *
51   	 * The objective function is then modified to \f$f(x) + M\theta\f$, where \f$M\f$ is a parameter for penalizing the
52   	 * distance of solutions from the input solution \f$\hat{x}\f$.
53   	 *
54   	 * If a new incumbent solution is found by this heuristic, then the Trust Region heuristic is immediately
55   	 * re-executed with this new incumbent solution.
56   	 */
57   	
58   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
59   	
60   	#ifndef __SCIP_HEUR_TRUSTREGION_H__
61   	#define __SCIP_HEUR_TRUSTREGION_H__
62   	
63   	#include "scip/def.h"
64   	#include "scip/type_retcode.h"
65   	#include "scip/type_scip.h"
66   	
67   	#ifdef __cplusplus
68   	extern "C" {
69   	#endif
70   	
71   	/** creates local branching primal heuristic and includes it in SCIP
72   	 *
73   	 *  @ingroup PrimalHeuristicIncludes
74   	 */
75   	SCIP_EXPORT
76   	SCIP_RETCODE SCIPincludeHeurTrustregion(
77   	   SCIP*                 scip                /**< SCIP data structure */
78   	   );
79   	
80   	#ifdef __cplusplus
81   	}
82   	#endif
83   	
84   	#endif
85