Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities

被引：11

作者：

Gschwind, Timo ^{[1
]}

Irnich, Stefan ^{[1
]}

机构：

[1] Johannes Gutenberg Univ Mainz, Gutenberg Sch Management & Econ, Chair Logist Management, Jakob Welder Weg 9, D-55128 Mainz, Germany

来源：

OR SPECTRUM | 2017年 / 39卷 / 02期

关键词：

Column generation; Dual inequalities; Stabilization; OPTIMIZATION;

D O I：

10.1007/s00291-016-0463-x

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We present two new methods to stabilize column-generation algorithms for the temporal knapsack problem (TKP). Caprara et al. (INFORMS J Comp 25(3):560-571, 2013] were the first to suggest the use of branch-and-price algorithms for Dantzig-Wolfe reformulations of the TKP. Herein, the respective pricing problems are smaller-sized TKP that can be solved with a general-purpose MIP solver or by dynamic programming. Our stabilization methods are tailored to the TKP as they use (deep) dual-optimal inequalities, that is, inequalities known to be fulfilled by all (at least some) optimal dual solutions to the linear relaxation. Extensive computational tests reveal that both new stabilization techniques are helpful. Several previously unsolved instances are now solved to proven optimality.

引用

页码：541 / 556

页数：16

共 50 条

[21] Using extra dual cuts to accelerate column generation
de Carvalho, JMV
INFORMS JOURNAL ON COMPUTING, 2005, 17 (02) : 175 - 182
[22] USING COLUMN GENERATION TO SOLVE A COAL BLENDING PROBLEM
Auray, Stephane
de Wolf, Daniel
Smeers, Yves
RAIRO-OPERATIONS RESEARCH, 2015, 49 (01) : 15 - 37
[23] Solving the Coarseness Problem by ILP Using Column Generation
Sapucaia, Allan
de Rezende, Pedro J.
de Souza, Cid C.
COMPUTATIONAL SCIENCE AND ITS APPLICATIONS, ICCSA 2021, PT V, 2021, 12953 : 30 - 45
[24] Shipment planning at oil refineries using column generation and valid inequalities
Persson, JA
Göthe-Lundgren, M
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2005, 163 (03) : 631 - 652
[25] Combined column-and-row-generation for the optimal communication spanning tree problem
Tilk, Christian
Irnich, Stefan
COMPUTERS & OPERATIONS RESEARCH, 2018, 93 : 113 - 122
[26] Optimal VNF Placement and Traffic Steering using Column Generation
Gupta, Devyani
Kuri, Joy
2020 IEEE 9TH INTERNATIONAL CONFERENCE ON CLOUD NETWORKING (CLOUDNET), 2020,
[27] Solving a continuous local access network design problem with a stabilized central column generation approach
Trampont, M.
Destre, C.
Faye, A.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2011, 214 (03) : 546 - 558
[28] Chaff-Points Generation Using Knapsack Problem Resolution in Fingerprint Fuzzy Vault
Dellys, Hachemi Nabil
Sliman, Layth
Artabaz, Saliha
Benatchba, Karima
Koudil, Mouloud
PROCEEDINGS OF THE 16TH INTERNATIONAL CONFERENCE ON HYBRID INTELLIGENT SYSTEMS (HIS 2016), 2017, 552 : 507 - 516
[29] A DUAL ASCENT AND COLUMN GENERATION HEURISTIC FOR THE DISCRETE LOTSIZING AND SCHEDULING PROBLEM WITH SETUP TIMES
CATTRYSSE, D
SALOMON, M
KUIK, R
VANWASSENHOVE, LN
MANAGEMENT SCIENCE, 1993, 39 (04) : 477 - 486
[30] Solving the skiving stock problem by a combination of stabilized column generation and the Reflect Arc-Flow model
Korbacher, Laura
Irnich, Stefan
Martinovic, John
Strasdat, Nico
DISCRETE APPLIED MATHEMATICS, 2023, 334 : 145 - 162

← 1 2 3 4 5 →