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 sepa_mcf.h 26 * @ingroup SEPARATORS 27 * @brief multi-commodity-flow network cut separator 28 * @author Tobias Achterberg 29 * @author Christian Raack 30 * 31 * We try to identify a multi-commodity flow structure in the LP relaxation of the 32 * following type: 33 * 34 * (1) sum_{a in delta^+(v)} f_a^k - sum_{a in delta^-(v)} f_a^k <= -d_v^k for all v in V and k in K 35 * (2) sum_{k in K} f_a^k - c_a x_a <= 0 for all a in A 36 * 37 * Constraints (1) are flow conservation constraints, which say that for each commodity k and node v the 38 * outflow (delta^+(v)) minus the inflow (delta^-(v)) of a node v must not exceed the negative of the demand of 39 * node v in commodity k. To say it the other way around, inflow minus outflow must be at least equal to the demand. 40 * Constraints (2) are the arc capacity constraints, which say that the sum of all flow over an arc a must not 41 * exceed its capacity c_a x_a, with x being a binary or integer variable. 42 * c_a x_a does not need to be a single product of a capacity and an integer variable; we also accept general scalar 43 * products. 44 */ 45 46 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/ 47 48 #ifndef __SCIP_SEPA_MCF_H__ 49 #define __SCIP_SEPA_MCF_H__ 50 51 #include "scip/def.h" 52 #include "scip/type_retcode.h" 53 #include "scip/type_scip.h" 54 #ifdef __cplusplus 55 extern "C" { 56 #endif 57 58 /** creates the mcf separator and includes it in SCIP 59 * 60 * @ingroup SeparatorIncludes 61 */ 62 SCIP_EXPORT 63 SCIP_RETCODE SCIPincludeSepaMcf( 64 SCIP* scip /**< SCIP data structure */ 65 ); 66 67 #ifdef __cplusplus 68 } 69 #endif 70 71 #endif 72