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

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

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.

Exact and approximation algorithms for a soft rectangle packing problem

Optimization ◽  
2012 ◽  
Vol 63 (11) ◽  
pp. 1637-1663 ◽  
Author(s):  
Armin Fügenschuh ◽  
Konstanty Junosza-Szaniawski ◽  
Zbigniew Lonc
Keyword(s):  
Approximation Algorithms ◽  
Packing Problem ◽  
Rectangle Packing ◽  
Rectangle Packing Problem
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