A dynamic programming algorithm for the bilevel knapsack problem

被引：38

作者：

Brotcorne, Luce ^{[1
]}

Hanafi, Said ^{[1
]}

Mansi, Raid ^{[1
]}

机构：

[1] UVHC Le Mt Houy, LAMIH ROI, ISTV2, F-59313 Valenciennes 9, France

来源：

OPERATIONS RESEARCH LETTERS | 2009年 / 37卷 / 03期

关键词：

Knapsack problem; Bilevel programming; Dynamic programming;

D O I：

10.1016/j.orl.2009.01.007

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 propose an efficient dynamic programming algorithm for solving a bilevel program where the leader controls the capacity of a knapsack, and the follower solves the resulting knapsack problem. We propose new recursive rules and show how to solve the problem as a sequence of two standard knapsack problems. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：215 / 218

页数：4

共 50 条

[1] A dynamic programming algorithm for the Knapsack Problem with Setup
Chebil, Khalil
Khemakhem, Mahdi
[J]. COMPUTERS & OPERATIONS RESEARCH, 2015, 64 : 40 - 50
[2] Integer Programming Formulation of the Bilevel Knapsack Problem
Mansi, R.
Hanafi, S.
Brotcorne, L.
[J]. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2010, 5 (07) : 116 - 121
[3] One-level reformulation of the bilevel Knapsack problem using dynamic programming
Brotcorne, Luce
Hanafi, Said
Mansi, Raid
[J]. DISCRETE OPTIMIZATION, 2013, 10 (01) : 1 - 10
[4] A faster algorithm for the continuous bilevel knapsack problem
Fischer, Dennis
Woeginger, Gerhard J.
[J]. OPERATIONS RESEARCH LETTERS, 2020, 48 (06) : 784 - 786
[5] A polynomial algorithm for a continuous bilevel knapsack problem
Carvalho, Margarida
Lodi, Andrea
Marcotte, Patrice
[J]. OPERATIONS RESEARCH LETTERS, 2018, 46 (02) : 185 - 188
[6] The Parallel Processing Approach to the Dynamic Programming Algorithm of Knapsack Problem
Sin, Si Thu Thant
[J]. PROCEEDINGS OF THE 2021 IEEE CONFERENCE OF RUSSIAN YOUNG RESEARCHERS IN ELECTRICAL AND ELECTRONIC ENGINEERING (ELCONRUS), 2021, : 2252 - 2256
[7] AN ALGORITHM FOR THE DISCRETE BILEVEL PROGRAMMING PROBLEM
BARD, JF
MOORE, JT
[J]. NAVAL RESEARCH LOGISTICS, 1992, 39 (03) : 419 - 435
[8] A lifted-space dynamic programming algorithm for the Quadratic Knapsack Problem
Fomeni, Franklin Djeumou
[J]. DISCRETE APPLIED MATHEMATICS, 2023, 335 : 52 - 68
[9] A fast combinatorial algorithm for the bilevel knapsack problem with interdiction constraints
Weninger, Noah
Fukasawa, Ricardo
[J]. MATHEMATICAL PROGRAMMING, 2024,
[10] A Fast Combinatorial Algorithm for the Bilevel Knapsack Problem with Interdiction Constraints
Weninger, Noah
Fukasawa, Ricardo
[J]. INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, IPCO 2023, 2023, 13904 : 438 - 452

← 1 2 3 4 5 →