SCIP

Solving Constraint Integer Programs

heur_multistart.h
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1 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
2 /* */
3 /* This file is part of the program and library */
4 /* SCIP --- Solving Constraint Integer Programs */
5 /* */
7 /* fuer Informationstechnik Berlin */
8 /* */
10 /* */
12 /* along with SCIP; see the file COPYING. If not visit scip.zib.de. */
13 /* */
14 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
15
16 /**@file heur_multistart.h
17  * @ingroup PRIMALHEURISTICS
18  * @brief multistart heuristic for convex and nonconvex MINLPs
19  * @author Benjamin Mueller
20  *
21  * The heuristic applies multiple NLP local searches to a mixed-integer nonlinear program with, probably nonconvex,
22  * constraints of the form \f$g_j(x) \le 0\f$. The algorithm tries to identify clusters which approximate the boundary
23  * of the feasible set of the continuous relaxation by sampling and improving randomly generated points. For each
24  * cluster we use a local search heuristic to find feasible solutions. The algorithm consists of the following four
25  * steps:
26  *
27  * 1. sample points
28  *
29  * Sample random points \f$x^1, \ldots, x^n \f$ in the box \f$[\ell,u] \f$. For an unbounded variable \f$x_i \f$
30  * we consider \f$[\ell_i,\ell_i + \alpha], [u_i - \alpha,u_i], \f$ or \f$[-\alpha / 2, \alpha / 2]\f$ for an \f$31 * \alpha > 0 \f$ depending on which bound is infinite.
32  *
33  * 2. reduce infeasibility
34  *
35  * For each point \f$x^i \f$ we use a gradient descent method to reduce the maximum infeasibility. We first compute
36  *
37  * \f[
38  * d_j = -\frac{g_j(x^i)}{||\nabla g_j(x^i)||^2} \nabla g_j(x^i)
39  * \f]
40  *
41  * and update the current point \f$x^i \f$ with
42  *
43  * \f[
44  * x^i := x^i + \frac{1}{n_j} \sum_{j} d_j
45  * \f]
46  *
47  * where \f$n_j \f$ is the number of strictly positive \f$d_j \f$. The algorithm is called Constraint Consensus
48  * Method and has been introduced by <a
49  * href="http://www.sce.carleton.ca/faculty/chinneck/docs/ConstraintConsensusJoC.pdf">here </a>.
50  *
51  * 3. cluster points
52  *
53  * We use a greedy algorithm to all of the resulting points of step 3. to find clusters which (hopefully) approximate
54  * the boundary of the feasible set locally. Points with a too large violations will be filtered.
55  *
56  * 4. solve sub-problems
57  *
58  * Depending on the current setting, we solve a sub-problem for each identified cluster. The default strategy is to
59  * compute a starting point for the sub-NLP heuristic (see @ref heur_subnlp.h) by using a linear combination of the
60  * points in a cluster \f$C \f$, i.e.,
61  *
62  * \f[
63  * s := \sum_{x \in C} \lambda_x x
64  * \f]
65  *
66  * Since the sub-NLP heuristic requires a starting point which is integer feasible we round each fractional
67  * value \f$s_i \f$ to its closest integer.
68  */
69
70
71 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
72
73 #ifndef __SCIP_HEUR_MULTISTART_H__
74 #define __SCIP_HEUR_MULTISTART_H__
75
76 #include "scip/def.h"
77 #include "scip/type_retcode.h"
78 #include "scip/type_scip.h"
79
80 #ifdef __cplusplus
81 extern "C" {
82 #endif
83
84 /** creates the multistart primal heuristic and includes it in SCIP
85  *
86  * @ingroup PrimalHeuristicIncludes
87  */
90  SCIP* scip /**< SCIP data structure */
91  );
92
93 #ifdef __cplusplus
94 }
95 #endif
96
97 #endif
#define SCIP_EXPORT
Definition: def.h:98
enum SCIP_Retcode SCIP_RETCODE
Definition: type_retcode.h:53
type definitions for return codes for SCIP methods
SCIP_EXPORT SCIP_RETCODE SCIPincludeHeurMultistart(SCIP *scip)
type definitions for SCIP&#39;s main datastructure
common defines and data types used in all packages of SCIP