1 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 2 /* */ 3 /* This file is part of the program and library */ 4 /* SCIP --- Solving Constraint Integer Programs */ 5 /* */ 6 /* Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB) */ 7 /* */ 8 /* Licensed under the Apache License, Version 2.0 (the "License"); */ 9 /* you may not use this file except in compliance with the License. */ 10 /* You may obtain a copy of the License at */ 11 /* */ 12 /* http://www.apache.org/licenses/LICENSE-2.0 */ 13 /* */ 14 /* Unless required by applicable law or agreed to in writing, software */ 15 /* distributed under the License is distributed on an "AS IS" BASIS, */ 16 /* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */ 17 /* See the License for the specific language governing permissions and */ 18 /* limitations under the License. */ 19 /* */ 20 /* You should have received a copy of the Apache-2.0 license */ 21 /* along with SCIP; see the file LICENSE. If not visit scipopt.org. */ 22 /* */ 23 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 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 98 SCIP_RETCODE SCIPincludeHeurMultistart( 99 SCIP* scip /**< SCIP data structure */ 100 ); 101 102 #ifdef __cplusplus 103 } 104 #endif 105 106 #endif 107