.png){kind=icon}
返回
Searching for optimal integer solutions to set partitioning problems using column generation
.png){kind=icon}
OA
AI
DOI：10.1111/itor.12050.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
In this paper, we describe a new approach to increase the possibility of finding integer feasible columns to a set partitioning problem (SPP) directly in solving the linear programming (LP) relaxation using column generation. Traditionally, column generation is aimed to solve the LP-relaxation as quickly as possible without any concern for the integer properties of the columns formed. In our approach, we aim to generate columns forming an optimal integer solution while simultaneously solving the LP-relaxation. Using this approach, we can improve the possibility of finding integer solutions by heuristics at each node in the branch-and-bound search. In addition, we improve the possibility of finding high-quality integer solutions in cases where only the columns in the root node are used to solve the problem. The basis of our approach is a subgradient technique applied to a Lagrangian dual formulation of the SPP extended with an additional surrogate constraint. This extra constraint is not relaxed and is used to better control the subgradient evaluations and how the multiplier values are computed. The column generation is then directed, via the multipliers, to construct columns that form feasible integer solutions. Computational experiments show that we can generate optimal integer columns in a large set of well-known test problems as compared to both standard and stabilized column generation, and simultaneously keep the number of columns smaller than standard column generation. This is also supported by tests on a case study with work-shift generation.
Keyword:
integer programming
column generation
lagrangian relaxation
heuristic
set partitioning problem
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
2.9
论文数:
1.8K
被引数:
3.7K
机构
引用论文
分享收藏分享收藏The Prognostic Significance of Uric Acid/Albumin Ratio in Patients with Aortic Stenosis Following Transcatheter Aortic Valve Implantation for Major Adverse Cardiac and Cerebral Events主动脉狭窄患者经导管主动脉瓣植入术后尿酸/白蛋白比值对主要心血管和脑血管不良事件的预后意义.png)
MedicinaOAAI
MedicinaIF0
OAAI分享收藏
查看更多内容