A Core Heuristic and the Branch-and-Price Method for a Bin Packing Problem with a Color Constraint

2018 ◽  
pp. 309-320 ◽  
Author(s):  
Artem Kondakov ◽  
Yury Kochetov
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Branch And Price ◽  
Bin Packing Problem

Branch-and-price and beam search algorithms for the Variable Cost and Size Bin Packing Problem with optional items

2012 ◽  
Vol 222 (1) ◽  
pp. 125-141 ◽  
Author(s):  
Mauro Maria Baldi ◽  
Teodor Gabriel Crainic ◽  
Guido Perboli ◽  
Roberto Tadei
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Search Algorithms ◽  
Variable Cost ◽  
Beam Search ◽  
Branch And Price ◽  
Bin Packing Problem

A Branch-and-Price Algorithm for the Bin Packing Problem with Conflicts

2011 ◽  
Vol 23 (3) ◽  
pp. 404-415 ◽  
Author(s):  
Samir Elhedhli ◽  
Lingzi Li ◽  
Mariem Gzara ◽  
Joe Naoum-Sawaya
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Branch And Price ◽  
Bin Packing Problem ◽  
Price Algorithm

Models and Algorithms for the Bin-Packing Problem with Minimum Color Fragmentation

2021 ◽  
Author(s):  
Saharnaz Mehrani ◽  
Carlos Cardonha ◽  
David Bergman
Keyword(s):  
Integer Programming ◽  
Bin Packing ◽  
Packing Problem ◽  
Mixed Integer ◽  
Decision Diagrams ◽  
Branch And Price ◽  
Recursive Decomposition ◽  
Computational Performance ◽  
Bin Packing Problem ◽  
Decomposition Strategies

In the bin-packing problem with minimum color fragmentation (BPPMCF), we are given a fixed number of bins and a collection of items, each associated with a size and a color, and the goal is to avoid color fragmentation by packing items with the same color within as few bins as possible. This problem emerges in areas as diverse as surgical scheduling and group event seating. We present several optimization models for the BPPMCF, including baseline integer programming formulations, alternative integer programming formulations based on two recursive decomposition strategies that utilize decision diagrams, and a branch-and-price algorithm. Using the results from an extensive computational evaluation on synthetic instances, we train a decision tree model that predicts which algorithm should be chosen to solve a given instance of the problem based on a collection of derived features. Our insights are validated through experiments on the aforementioned applications on real-world data. Summary of Contribution: In this paper, we investigate a colored variant of the bin-packing problem. We present and evaluate several exact mixed-integer programming formulations to solve the problem, including models that explore recursive decomposition strategies based on decision diagrams and a set partitioning model that we solve using branch and price. Our results show that the computational performance of the algorithms depends on features of the input data, such as the average number of items per bin. Our algorithms and featured applications suggest that the problem is of practical relevance and that instances of reasonable size can be solved efficiently.

A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint

2008 ◽  
Vol 179 (1) ◽  
pp. 221-241 ◽  
Author(s):  
Andrea Bettinelli ◽  
Alberto Ceselli ◽  
Giovanni Righini
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Branch And Price ◽  
Variable Size ◽  
Bin Packing Problem ◽  
Price Algorithm

A New Branch-and-Price-and-Cut Algorithm for One-Dimensional Bin-Packing Problems

2020 ◽  
Vol 32 (2) ◽  
pp. 428-443
Author(s):  
Lijun Wei ◽  
Zhixing Luo ◽  
Roberto Baldacci ◽  
Andrew Lim
Keyword(s):  
Bin Packing ◽  
Large Family ◽  
Exact Algorithm ◽  
Packing Problem ◽  
Set Partitioning ◽  
Branch And Price ◽  
Packing Problems ◽  
One Dimensional ◽  
Bin Packing Problem ◽  
The One

In this paper, a new branch-and-price-and-cut algorithm is proposed to solve the one-dimensional bin-packing problem (1D-BPP). The 1D-BPP is one of the most fundamental problems in combinatorial optimization and has been extensively studied for decades. Recently, a set of new 500 test instances were proposed for the 1D-BPP, and the best exact algorithm proposed in the literature can optimally solve 167 of these new instances, with a time limit of 1 hour imposed on each execution of the algorithm. The exact algorithm proposed in this paper is based on the classical set-partitioning model for the 1DBPPs and the subset row inequalities. We describe an ad hoc label-setting algorithm to solve the pricing problem, dominance, and fathoming rules to speed up its computation and a new primal heuristic. The exact algorithm can easily handle some practical constraints, such as the incompatibility between the items, and therefore, we also apply it to solve the one-dimensional bin-packing problem with conflicts (1D-BPPC). The proposed method is tested on a large family of 1D-BPP and 1D-BPPC classes of instances. For the 1D-BPP, the proposed method can optimally solve 237 instances of the new set of difficult instances; the largest instance involves 1,003 items and bins of capacity 80,000. For the 1D-BPPC, the experiments show that the method is highly competitive with state-of-the-art methods and that it successfully closed several open 1D-BPPC instances.

scholarly journals A branch-and-price algorithm for the temporal bin packing problem

2020 ◽  
Vol 114 ◽  
pp. 104825
Author(s):  
Mauro Dell’Amico ◽  
Fabio Furini ◽  
Manuel Iori
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Branch And Price ◽  
Bin Packing Problem ◽  
Price Algorithm
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