scholarly journals Two and three-dimensional bin packing problems : an efficient implementation of evolutionary algorithms

2018 ◽  
Author(s):  
◽  
Andile Ntanjana
Keyword(s):  
Genetic Algorithm ◽  
Polynomial Time ◽  
Heuristic Algorithm ◽  
Bin Packing ◽  
Optimization Problems ◽  
Research Work ◽  
Three Dimensional ◽  
Second Phase ◽  
Packing Problems ◽  
Elitist Strategy

The present research work deals with the implementation of heuristics and genetic algo- rithms to solve various bin packing problems (BPP). Bin packing problems are a class of optimization problems that have numerous applications in the industrial world, ranging from efficient cutting of material to packing various items in a larger container. Bin packing problems are known to be non-deterministic polynomial-time hard (NP-hard), and hence it is impossible to solve them exactly in polynomial time. Thus heuristics are very important to design practical algorithms for such problems. In this research we avoid the use of linear programming because we consider it to be a very cumbersome approach for analysing these types of problems and instead we proposed a simple and very efficient algorithm which is a combination of the fi fi heuristic algorithm in combination with the genetic algorithm, to solve the two and three – dimensional bin packing problems. The packing was carried out in two phases, wherein the fi phase the bins are packed by means of the fi fi heuristic algorithm with the help of other auxiliary techniques, and in the second phase the genetic algorithm is implemented. The purpose of the second phase is to improve the initial arrangements by performing combinatorial optimization for either a limited number of bins or the whole set at one time without destroying the original pattern (elitist strategy). The programming code developed can be used to write high-speed and capable software, which can be used in real-time applications. To conclude, the developed optimization ap- proach signifi tly helps to handle the bin packing problem. Numerical results obtained by optimizing existing industrial problems demonstrated that in many cases it was possible to achieve the optimum solution within only a few seconds, whereas for large-scale complex problems the result was near optimum efficiency over 90% within the same period of time.

The Improvement of a Hybrid Genetic Algorithm for Three Dimensional Bin-Packing Problems

2012 ◽  
Vol 200 ◽  
pp. 470-473
Author(s):  
Zhen Zhai ◽  
Li Chen ◽  
Xiao Min Han
Keyword(s):  
Genetic Algorithm ◽  
Bin Packing ◽  
Hybrid Genetic Algorithm ◽  
Three Dimensional ◽  
Packing Problem ◽  
Flow Process ◽  
Packing Problems ◽  
Loading Problem ◽  
The Cost ◽  
Process Diagrams

The multi-constrained bi-objective bin packing problem has many extensive applications. In the loading section of logistics it has mainly been transported by truck. The cost of transportation is not only determined by the bin space utilization, but also by the number of vehicles in transporta¬tion utilization. The type of items and bins is introduced in the mathematical model, as well as the volume of the items. In this paper, the hybrid genetic algorithm which tabu and simulated annealed rules are added for complex container-loading problem is studied. The effective coding and decod-ing method together with flow process diagrams are given.

An improved nature inspired meta-heuristic algorithm for 1-D bin packing problems

2018 ◽  
Vol 22 (5-6) ◽  
pp. 1117-1132 ◽  
Author(s):  
Mohamed Abdel-Basset ◽  
Gunasekaran Manogaran ◽  
Laila Abdel-Fatah ◽  
Seyedali Mirjalili
Keyword(s):  
Heuristic Algorithm ◽  
Bin Packing ◽  
Packing Problems

scholarly journals Automating the Packing Heuristic Design Process with Genetic Programming

2012 ◽  
Vol 20 (1) ◽  
pp. 63-89 ◽  
Author(s):  
Edmund K. Burke ◽  
Matthew R. Hyde ◽  
Graham Kendall ◽  
John Woodward
Keyword(s):  
Genetic Programming ◽  
Design Process ◽  
Design Methodology ◽  
Bin Packing ◽  
Three Dimensional ◽  
Programming System ◽  
Problem Type ◽  
Packing Problems ◽  
Design Heuristics ◽  
Design Heuristic

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains.

scholarly journals A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Mhand Hifi ◽  
Rym M'Hallah
Keyword(s):  
Literature Review ◽  
Branch And Bound ◽  
Euclidean Plane ◽  
Optimization Problems ◽  
Relevant Literature ◽  
Three Dimensional ◽  
Sphere Packing ◽  
Nonconvex Minimization ◽  
Packing Problems ◽  
Computer Aided

This paper reviews the most relevant literature on efficient models and methods for packing circular objects/items into Euclidean plane regions where the objects/items and regions are either two- or three-dimensional. These packing problems are NP hard optimization problems with a wide variety of applications. They have been tackled using various approaches-based algorithms ranging from computer-aided optimality proofs, to branch-and-bound procedures, to constructive approaches, to multi-start nonconvex minimization, to billiard simulation, to multiphase heuristics, and metaheuristics.

scholarly journals Erratum to “The Three-Dimensional Bin Packing Problem”: Robot-Packable and Orthogonal Variants of Packing Problems

2005 ◽  
Vol 53 (4) ◽  
pp. 735-736 ◽  
Author(s):  
Edgar den Boef ◽  
Jan Korst ◽  
Silvano Martello ◽  
David Pisinger ◽  
Daniele Vigo
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Packing Problems ◽  
Bin Packing Problem

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

scholarly journals A factor graph based genetic algorithm

2014 ◽  
Vol 24 (3) ◽  
pp. 621-633 ◽  
Author(s):  
B. Hoda Helmi ◽  
Adel T. Rahmani ◽  
Martin Pelikan
Keyword(s):  
Genetic Algorithm ◽  
Polynomial Time ◽  
Mathematical Analysis ◽  
Matrix Factorization ◽  
Optimization Problems ◽  
Factor Graph ◽  
The Matrix ◽  
Separable Problems ◽  
Linkage Learning ◽  
Non Negative Matrix Factorization

Abstract We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems are provided as support for the mathematical analysis of the approach. The experiments show that FGGA is capable of learning linkages and solving the optimization problems in polynomial time with a polynomial number of evaluations.

Effective Data Structure for the Multidimensional Orthogonal Bin Packing Problems

2014 ◽  
Vol 962-965 ◽  
pp. 2868-2871 ◽  
Author(s):  
Alexander V. Chekanin ◽  
Vladislav A. Chekanin
Keyword(s):  
Data Structure ◽  
Linked Data ◽  
Bin Packing ◽  
High Efficiency ◽  
Optimization Problems ◽  
Packing Problem ◽  
Strong Sense ◽  
Np Hard ◽  
Packing Problems ◽  
Orthogonal Packing Problem

The actual in industry multidimensional orthogonal packing problem is considered in the article. Solution of a large number of different practical optimization problems, including resources saving problem, optimization problems in logistics, scheduling and planning comes down to the orthogonal packing problem which is NP-hard in strong sense. One of the indicators characterizing the efficiency of packing constructing algorithm is the efficiency of the used data structure. In the article a multilevel linked data structure that increases the speed of constructing of a packing is proposed. The carried out computational experiments show the high efficiency of the new data structure. Multilevel linked data structure is applicable for multidimensional orthogonal bin packing problems any kind.

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