scholarly journals Corner occupying theorem for the two-dimensional integral rectangle packing problem

2012 ◽  
Vol 55 (11) ◽  
pp. 2466-2472
Author(s):  
WenQi Huang ◽  
Tao Ye ◽  
DuanBing Chen
Keyword(s):  
Packing Problem ◽  
Two Dimensional ◽  
Rectangle Packing ◽  
Dimensional Integral ◽  
Rectangle Packing Problem

scholarly journals A new nonlinear model for the two-dimensional rectangle packing problem

2013 ◽  
Vol 93 (107) ◽  
pp. 95-107
Author(s):  
Aleksandar Savic ◽  
Jozef Kratica ◽  
Vladimir Filipovic
Keyword(s):  
Nonlinear Programming ◽  
Piecewise Linear ◽  
Packing Problem ◽  
Linear Formulation ◽  
Mixed Integer ◽  
Two Dimensional ◽  
Programming Formulation ◽  
Real Numbers ◽  
Rectangle Packing ◽  
Rectangle Packing Problem

This paper deals with the rectangle packing problem, of filling a big rectangle with smaller rectangles, while the rectangle dimensions are real numbers. A new nonlinear programming formulation is presented and the validity of the formulation is proved. In addition, two cases of the problem are presented, with and without rotation of smaller rectangles by 90?. The mixed integer piecewise linear formulation derived from the model is given, but with a simple form of the objective function.

Solving Two-Dimensional Rectangle Packing Problem Using Nature-Inspired Metaheuristic Algorithms

2018 ◽  
Vol 03 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Amandeep Kaur Virk ◽  
Kawaljeet Singh
Keyword(s):  
Genetic Algorithm ◽  
Tabu Search ◽  
Search Algorithm ◽  
Packing Problem ◽  
Cuckoo Search ◽  
Metaheuristic Algorithms ◽  
Two Dimensional ◽  
Rectangle Packing ◽  
Metaheuristic Methods ◽  
Rectangle Packing Problem

This paper applies cuckoo search and bat metaheuristic algorithms to solve two-dimensional non-guillotine rectangle packing problem. These algorithms have not been found to be used before in the literature to solve this important industrial problem. The purpose of this work is to explore the potential of these new metaheuristic methods and to check whether they can contribute in enhancing the performance of this problem. Standard benchmark test data has been used to solve the problem. The performance of these algorithms was measured and compared with genetic algorithm and tabu search techniques which can be found to be used widely in the literature to solve this problem. Good optimal solutions were obtained from all the techniques and the new metaheuristic algorithms performed better than genetic algorithm and tabu search. It was seen that cuckoo search algorithm excels in performance as compared to the other techniques.

An effective quasi-human based heuristic for solving the rectangle packing problem

2002 ◽  
Vol 141 (2) ◽  
pp. 341-358 ◽  
Author(s):  
Yu-Liang Wu ◽  
Wenqi Huang ◽  
Siu-chung Lau ◽  
C.K Wong ◽  
Gilbert H Young
Keyword(s):  
Packing Problem ◽  
Rectangle Packing ◽  
Rectangle Packing Problem

A NEW HEURISTIC ALGORITHM FOR CONSTRAINED RECTANGLE-PACKING PROBLEM

2007 ◽  
Vol 24 (04) ◽  
pp. 463-478 ◽  
Author(s):  
DUANBING CHEN ◽  
WENQI HUANG
Keyword(s):  
Heuristic Algorithm ◽  
Heuristic Algorithms ◽  
Packing Problem ◽  
Industrial Applications ◽  
Rectangle Packing ◽  
Simulated Annealing Genetic Algorithm ◽  
Rectangular Container ◽  
Glass Cutting ◽  
Integrated Performance ◽  
Rectangle Packing Problem

The constrained rectangle-packing problem is the problem of packing a subset of rectangles into a larger rectangular container, with the objective of maximizing the layout value. It has many industrial applications such as shipping, wood and glass cutting, etc. Many algorithms have been proposed to solve it, for example, simulated annealing, genetic algorithm and other heuristic algorithms. In this paper a new heuristic algorithm is proposed based on two strategies: the rectangle selecting strategy and the rectangle packing strategy. We have applied the algorithm to 21 smaller, 630 larger and other zero-waste instances. The computational results demonstrate that the integrated performance of the algorithm is rather satisfying and the algorithm developed is fairly efficient for solving the constrained rectangle-packing problem.

4-Block heuristic for the rectangle packing problem

1998 ◽  
Vol 108 (3) ◽  
pp. 509-526 ◽  
Author(s):  
Gubtram Scheithauer ◽  
Uta Sommerweiß
Keyword(s):  
Packing Problem ◽  
Rectangle Packing ◽  
Rectangle Packing Problem

An Ising model mapping to solve rectangle packing problem

2018 ◽  
Author(s):  
Kotaro Terada ◽  
Daisuke Oku ◽  
Sho Kanamaru ◽  
Shu Tanaka ◽  
Masato Hayashi ◽  
...  
Keyword(s):  
Ising Model ◽  
Packing Problem ◽  
Rectangle Packing ◽  
Model Mapping ◽  
Rectangle Packing Problem
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