Scippy

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 */
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24 
25 /**@file heur_multistart.h
26  * @ingroup PRIMALHEURISTICS
27  * @brief multistart heuristic for convex and nonconvex MINLPs
28  * @author Benjamin Mueller
29  *
30  * The heuristic applies multiple NLP local searches to a mixed-integer nonlinear program with, probably nonconvex,
31  * constraints of the form \f$g_j(x) \le 0\f$. The algorithm tries to identify clusters which approximate the boundary
32  * of the feasible set of the continuous relaxation by sampling and improving randomly generated points. For each
33  * cluster we use a local search heuristic to find feasible solutions. The algorithm consists of the following four
34  * steps:
35  *
36  * 1. sample points
37  *
38  * 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$
39  * we consider \f$ [\ell_i,\ell_i + \alpha], [u_i - \alpha,u_i], \f$ or \f$ [-\alpha / 2, \alpha / 2]\f$ for an \f$
40  * \alpha > 0 \f$ depending on which bound is infinite.
41  *
42  * 2. reduce infeasibility
43  *
44  * For each point \f$ x^i \f$ we use a gradient descent method to reduce the maximum infeasibility. We first compute
45  *
46  * \f[
47  * d_j = -\frac{g_j(x^i)}{||\nabla g_j(x^i)||^2} \nabla g_j(x^i)
48  * \f]
49  *
50  * and update the current point \f$ x^i \f$ with
51  *
52  * \f[
53  * x^i := x^i + \frac{1}{n_j} \sum_{j} d_j
54  * \f]
55  *
56  * where \f$ n_j \f$ is the number of strictly positive \f$ d_j \f$. The algorithm is called Constraint Consensus
57  * Method and has been introduced by <a
58  * href="http://www.sce.carleton.ca/faculty/chinneck/docs/ConstraintConsensusJoC.pdf">here </a>.
59  *
60  * 3. cluster points
61  *
62  * We use a greedy algorithm to all of the resulting points of step 3. to find clusters which (hopefully) approximate
63  * the boundary of the feasible set locally. Points with a too large violations will be filtered.
64  *
65  * 4. solve sub-problems
66  *
67  * Depending on the current setting, we solve a sub-problem for each identified cluster. The default strategy is to
68  * compute a starting point for the sub-NLP heuristic (see @ref heur_subnlp.h) by using a linear combination of the
69  * points in a cluster \f$ C \f$, i.e.,
70  *
71  * \f[
72  * s := \sum_{x \in C} \lambda_x x
73  * \f]
74  *
75  * Since the sub-NLP heuristic requires a starting point which is integer feasible we round each fractional
76  * value \f$ s_i \f$ to its closest integer.
77  */
78 
79 
80 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
81 
82 #ifndef __SCIP_HEUR_MULTISTART_H__
83 #define __SCIP_HEUR_MULTISTART_H__
84 
85 #include "scip/def.h"
86 #include "scip/type_retcode.h"
87 #include "scip/type_scip.h"
88 
89 #ifdef __cplusplus
90 extern "C" {
91 #endif
92 
93 /** creates the multistart primal heuristic and includes it in SCIP
94  *
95  * @ingroup PrimalHeuristicIncludes
96  */
97 SCIP_EXPORT
99  SCIP* scip /**< SCIP data structure */
100  );
101 
102 #ifdef __cplusplus
103 }
104 #endif
105 
106 #endif
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
SCIP_RETCODE SCIPincludeHeurMultistart(SCIP *scip)
common defines and data types used in all packages of SCIP