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

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.

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