scholarly journals A Column-Generation and Branch-and-Cut Approach to the Bandwidth-Packing Problem

2006 ◽  
Vol 111 (2) ◽  
pp. 161 ◽  
Author(s):  
Christine Villa ◽  
Karla Hoffman
Keyword(s):  
Column Generation ◽  
Packing Problem ◽  
Branch And Cut ◽  
Bandwidth Packing

scholarly journals A hybrid VNS matheuristic for a bin packing problem with a color constraint

2021 ◽  
pp. 9-9
Author(s):  
Yury Kochetov ◽  
Arteam Kondakov
Keyword(s):  
Column Generation ◽  
Bin Packing ◽  
Packing Problem ◽  
Upper Bounds ◽  
Hard Problem ◽  
Generation Technique ◽  
Bin Packing Problem ◽  
New Variant ◽  
Finite Set ◽  
Np Hard Problem

We study a new variant of the bin packing problem with a color constraint. Given a finite set of items, each item has a set of colors. Each bin has a color capacity, the total number of colors for a bin is the unification of colors for its items and cannot exceed the bin capacity. We need to pack all items into the minimal number of bins. For this NP-hard problem we present approximability results and design a hybrid matheuristic based on the column generation technique. A hybrid VNS heuristic is applied to the pricing problem. The column generation method provides a lower bound and a core subset of the most promising bin patterns. Fast heuristics and exact solution for this core produce upper bounds. Computational experiments for test instances with number of items up to 500 illustrate the efficiency of the approach.

The Repacking Efficiency for Bandwidth Packing Problem

2007 ◽  
Vol E90-D (7) ◽  
pp. 1011-1017
Author(s):  
J. CHEN ◽  
Y. YANG ◽  
L. ZHOU
Keyword(s):  
Packing Problem ◽  
Bandwidth Packing

An Integer Programming Approach to the Bandwidth Packing Problem

1996 ◽  
Vol 42 (9) ◽  
pp. 1277-1291 ◽  
Author(s):  
Kyungchul Park ◽  
Seokhoon Kang ◽  
Sungsoo Park
Keyword(s):  
Integer Programming ◽  
Packing Problem ◽  
Programming Approach ◽  
Bandwidth Packing

scholarly journals Accelerating Column Generation via Flexible Dual Optimal Inequalities with Application to Entity Resolution

2020 ◽  
Vol 34 (02) ◽  
pp. 1593-1602
Author(s):  
Vishnu Suresh Lokhande ◽  
Shaofei Wang ◽  
Maneesh Singh ◽  
Julian Yarkony
Keyword(s):  
Column Generation ◽  
Packing Problem ◽  
Entity Resolution ◽  
Optimization Approach ◽  
Set Packing ◽  
Packing Problems ◽  
Correlation Clustering ◽  
Benchmark Datasets ◽  
Set Packing Problem ◽  
Optimal Inequalities

In this paper, we introduce a new optimization approach to Entity Resolution. Traditional approaches tackle entity resolution with hierarchical clustering, which does not benefit from a formal optimization formulation. In contrast, we model entity resolution as correlation-clustering, which we treat as a weighted set-packing problem and write as an integer linear program (ILP). In this case, sources in the input data correspond to elements and entities in output data correspond to sets/clusters. We tackle optimization of weighted set packing by relaxing integrality in our ILP formulation. The set of potential sets/clusters can not be explicitly enumerated, thus motivating optimization via column generation. In addition to the novel formulation, we also introduce new dual optimal inequalities (DOI), that we call flexible dual optimal inequalities, which tightly lower-bound dual variables during optimization and accelerate column generation. We apply our formulation to entity resolution (also called de-duplication of records), and achieve state-of-the-art accuracy on two popular benchmark datasets. Our F-DOI can be extended to other weighted set-packing problems.

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