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

2018 ◽  
Vol 52 (2) ◽  
pp. 391-414 ◽  
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.

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

2017 ◽  
Vol 1 (1) ◽  
pp. 35-49 ◽  
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.

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

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.

scholarly journals A Reduced Variable Neighborhood Search Approach to the Heterogeneous Vector Bin Packing Problem

2021 ◽  
Vol 50 (4) ◽  
pp. 808-826
Author(s):  
Đorđe Stakić ◽  
Miodrag Živković ◽  
Ana Anokić
Keyword(s):  
Variable Neighborhood Search ◽  
Bin Packing ◽  
Optimization Problems ◽  
Packing Problem ◽  
Neighborhood Search ◽  
Two Dimensional ◽  
Total Cost ◽  
Bin Packing Problem ◽  
Benchmark Instances ◽  
Search Approach

The two-dimensional heterogeneous vector bin packing problem (2DHet-VBPP) consists of packing the set of items into the set of various type bins, respecting their two resource limits. The problem is to minimize the total cost of all bins. The problem, known to be NP-hard, can be formulated as a pure integer linear program, but optimal solutions can be obtained by the CPLEX Optimizer engine only for small instances. This paper proposes a metaheuristic approach to the 2DHet-VBPP, based on Reduced variable neighborhood search (RVNS). All RVNS elements are adapted to the considered problem and many procedures are designed to improve efficiency of the method. As the Two-dimensional Homogeneous-VBPP (2DHom-VBPP) is more often treated, we considered also a special version of the RVNS algorithm to solve the 2DHom-VBPP. The results obtained and compared to both CPLEX results and results on benchmark instances from literature, justify the use of the RVNS algorithm to solve large instances of these optimization problems.

A new lower bound for the non-oriented two-dimensional bin-packing problem

2007 ◽  
Vol 35 (3) ◽  
pp. 365-373 ◽  
Author(s):  
François Clautiaux ◽  
Antoine Jouglet ◽  
Joseph El Hayek
Keyword(s):  
Lower Bound ◽  
Bin Packing ◽  
Packing Problem ◽  
Two Dimensional ◽  
Bin Packing Problem
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