New Pretreatment and Resolution Using the Bee Colony Optimization for the Two-Dimensional Bin Packing Problem

Bulletin of Mathematical Sciences and Applications ◽

10.18052/www.scipress.com/bmsa.14.13 ◽

2016 ◽

Vol 14 ◽

pp. 13-22

Author(s):

Aida Kenza Amara ◽

Bachir Djebbar

Keyword(s):

Bin Packing ◽

Heuristic Method ◽

Packing Problem ◽

Computational Results ◽

Two Dimensional ◽

Bee Colony ◽

Bin Packing Problem ◽

Bee Colony Optimization ◽

Minimum Number

The two-dimensional bin packing problem involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. In this paper, we propose and develop mathematically a new pretreatment for the oriented version of the problem in order to reduce its size, identify and value the lost spaces by increasing the size of some objects. A heuristic method based on the first-fit strategy adapted to this problem is proposed. We present an approach of resolution using the bee colony optimization. The computational results show the effectiveness of the pretreatment in reducing the number of bins.

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A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem

RAIRO - Operations Research ◽

10.1051/ro/2017019 ◽

2018 ◽

Vol 52 (2) ◽

pp. 391-414 ◽

Cited By ~ 3

Author(s):

Mehdi Serairi ◽

Mohamed Haouari

Keyword(s):

Lower Bounds ◽

Bin Packing ◽

Computational Study ◽

Packing Problem ◽

Large Set ◽

Two Dimensional ◽

Bin Packing Problem ◽

Benchmark Instances ◽

Empirical Performance ◽

Minimum Number

We address the two-dimensional bin packing problem with fixed orientation. This problem requires packing a set of small rectangular items into a minimum number of standard two-dimensional bins. It is a notoriously intractable combinatorial optimization problem and has numerous applications in packing and cutting. The contribution of this paper is twofold. First, we propose a comprehensive theoretical analysis of lower bounds and we elucidate dominance relationships. We show that a previously presented dominance result is incorrect. Second, we present the results of an extensive computational study that was carried out, on a large set of 500 benchmark instances, to assess the empirical performance of the lower bounds. We found that the so-called Carlier-Clautiaux-Moukrim lower bounds exhibits an excellent relative performance and yields the tightest value for all of the benchmark instances.

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Rectangular Bin-Packing Problem: a computational evaluation of 4 heuristics algorithms

U Porto Journal of Engineering ◽

10.24840/2183-6493_001.001_0005 ◽

2017 ◽

Vol 1 (1) ◽

pp. 35-49 ◽

Cited By ~ 2

Author(s):

Duarte Nuno Gonçalves Ferreira

Keyword(s):

Genetic Algorithm ◽

Optimization Problem ◽

Bin Packing ◽

Packing Problem ◽

Combinatorial Optimization Problem ◽

Two Dimensional ◽

Computational Evaluation ◽

Bin Packing Problem ◽

Benchmark Instances ◽

Minimum Number

The Rectangular Bin-packing Problem, also known as The Two-dimensional Bin-packing Problem (2DBPP), is a well-known combinatorial optimization problem which is the problem of orthogonally packing a given set of rectangles into a minimum number of two-dimensional rectangular bins. In this article we benchmark four heuristics: constructive, based on a First Fit Decreasing strategy, local search using a greedy packing First-Fit algorithm, Simulated Annealing with multiple cooling values and Genetic Algorithm. All implementations are written in Python, run using the Pypy environment and the new multiprocessing module. All implementations were tested using the Berkey and Wang and Martelo and Vigo Benchmark Instances.

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