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

Efficient lower bounds and heuristics for the variable cost and size bin packing problem

2011 ◽  
Vol 38 (11) ◽  
pp. 1474-1482 ◽  
Author(s):  
Teodor Gabriel Crainic ◽  
Guido Perboli ◽  
Walter Rei ◽  
Roberto Tadei
Keyword(s):  
Lower Bounds ◽  
Bin Packing ◽  
Packing Problem ◽  
Variable Cost ◽  
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

scholarly journals fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

2021 ◽  
Vol 24 (67) ◽  
pp. 71-89
Author(s):  
Jorge Herrera-Franklin ◽  
Alejandro Rosete ◽  
Milton García-Borroto
Keyword(s):  
Bin Packing ◽  
Solution Method ◽  
Optimization Problems ◽  
Real Life ◽  
Packing Problem ◽  
Variable Cost ◽  
Bin Packing Problem ◽  
Trade Offs ◽  
Np Hard Problem ◽  
The Cost

The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizing the cost of all bins used to pack a set of items. There are many real-life applications of the VCSBPP where the focus is to improve the efficiency of the solution method. In spite of the existence of fuzzy approaches to adapt other optimization problems to real life conditions, VCSBPP has not been extensively studied in terms of relaxations of the crisp conditions. In this sense, the fuzzy approaches for the VCSBPP varies from relaxing the capacity of the bins to the items weights. In this paper we address a non-explored side consisting in relaxing the set of items to be packed. Therefore, our main contribution is a fuzzy version of VCSBPP that allows incomplete packing. The proposed fuzzy VCSBPP is solved by a parametric approach. Particularly, a fast heuristic algorithm is introduced that allows to obtain a set of solutions with interesting trade-offs between cost and relaxation of the original crisp conditions. An experimental study is presented to explore the proposed fuzzy VCSBPP and its solution.

Sign in / Sign up

Export Citation Format

Share Document