scholarly journals An efficient heuristic algorithm for two-dimensional rectangular packing problem with central rectangle

2020 ◽  
Vol 16 (1) ◽  
pp. 495-510
Author(s):  
Mao Chen ◽  
◽  
Xiangyang Tang ◽  
Zhizhong Zeng ◽  
Sanya Liu
Keyword(s):  
Heuristic Algorithm ◽  
Packing Problem ◽  
Two Dimensional ◽  
Rectangular Packing

A New Bottom-Left-Fill Heuristic Algorithm for the Two-Dimensional Irregular Packing Problem

2006 ◽  
Vol 54 (3) ◽  
pp. 587-601 ◽  
Author(s):  
Edmund Burke ◽  
Robert Hellier ◽  
Graham Kendall ◽  
Glenn Whitwell
Keyword(s):  
Heuristic Algorithm ◽  
Packing Problem ◽  
Two Dimensional ◽  
Bottom Left

THE TWO-DIMENSIONAL PACKING PROBLEM FOR IRREGULAR OBJECTS

2004 ◽  
Vol 13 (03) ◽  
pp. 429-448 ◽  
Author(s):  
PING CHEN ◽  
ZHAOHUI FU ◽  
ANDREW LIM ◽  
BRIAN RODRIGUES
Keyword(s):  
Genetic Algorithms ◽  
Basic Problem ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Packing Problem ◽  
Two Dimensional ◽  
Linear Representations ◽  
Rectangular Packing ◽  
Work Done ◽  
Cutting Problems

Packing and cutting problems arise in a wide variety of industrial situations. The basic problem is that of determining a good arrangement of objects in a region without any overlap. Much research has been done on two and three dimensional rectangular packing while there has been little work done on irregular packing. In this work, we study the two-dimensional irregular packing problem and provide heuristic solutions which use rectilinear and piecewise-linear representations of objects. These heuristics include Genetic Algorithms and Tabu Search. Experimentation gives good results.

scholarly journals An Improved Adaptive Genetic Algorithm for Two-Dimensional Rectangular Packing Problem

2021 ◽  
Vol 11 (1) ◽  
pp. 413
Author(s):  
Yi-Bo Li ◽  
Hong-Bao Sang ◽  
Xiang Xiong ◽  
Yu-Rou Li
Keyword(s):  
Genetic Algorithm ◽  
Packing Problem ◽  
Global Perspective ◽  
Adaptive Genetic Algorithm ◽  
Two Dimensional ◽  
Filling Rate ◽  
Zero Waste ◽  
Population Evolution ◽  
Rectangular Packing ◽  
The Impact

This paper proposes the hybrid adaptive genetic algorithm (HAGA) as an improved method for solving the NP-hard two-dimensional rectangular packing problem to maximize the filling rate of a rectangular sheet. The packing sequence and rotation state are encoded in a two-stage approach, and the initial population is constructed from random generation by a combination of sorting rules. After using the sort-based method as an improved selection operator for the hybrid adaptive genetic algorithm, the crossover probability and mutation probability are adjusted adaptively according to the joint action of individual fitness from the local perspective and the global perspective of population evolution. The approach not only can obtain differential performance for individuals but also deals with the impact of dynamic changes on population evolution to quickly find a further improved solution. The heuristic placement algorithm decodes the rectangular packing sequence and addresses the two-dimensional rectangular packing problem through continuous iterative optimization. The computational results of a wide range of benchmark instances from zero-waste to non-zero-waste problems show that the HAGA outperforms those of two adaptive genetic algorithms from the related literature. Compared with some recent algorithms, this algorithm, which can be increased by up to 1.6604% for the average filling rate, has great significance for improving the quality of work in fields such as packing and cutting.

scholarly journals Solving the two-dimensional packing problem with m-M calculus

2011 ◽  
Vol 21 (1) ◽  
pp. 93-102 ◽  
Author(s):  
Aleksandar Savic ◽  
Tijana Sukilovic ◽  
Vladimir Filipovic
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Mathematical Formulation ◽  
Packing Problem ◽  
Linear Constraints ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Computational Performance ◽  
Non Linear ◽  
Rectangular Packing

This paper considers the two dimensional rectangular packing problem. The mathematical formulation is based on the optimization of a non-linear function with piecewise linear constraints with a small number of real variables. The presented method of m-M calculus finds all optimal solutions on small instances. Computational performance is good on smaller instances.

An efficient deterministic heuristic algorithm for the rectangular packing problem

2019 ◽  
Vol 137 ◽  
pp. 106097 ◽  
Author(s):  
Mao Chen ◽  
Chao Wu ◽  
Xiangyang Tang ◽  
Xicheng Peng ◽  
Zhizhong Zeng ◽  
...  
Keyword(s):  
Heuristic Algorithm ◽  
Packing Problem ◽  
Rectangular Packing
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