1 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 2 /* */ 3 /* This file is part of the program and library */ 4 /* SCIP --- Solving Constraint Integer Programs */ 5 /* */ 6 /* Copyright (C) 2002-2021 Konrad-Zuse-Zentrum */ 7 /* fuer Informationstechnik Berlin */ 8 /* */ 9 /* SCIP is distributed under the terms of the ZIB Academic License. */ 10 /* */ 11 /* You should have received a copy of the ZIB Academic License */ 12 /* along with SCIP; see the file COPYING. If not visit scipopt.org. */ 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 */ 88 SCIP_EXPORT 89 SCIP_RETCODE SCIPincludeHeurMultistart( 90 SCIP* scip /**< SCIP data structure */ 91 ); 92 93 #ifdef __cplusplus 94 } 95 #endif 96 97 #endif 98