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

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.

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A Reinforced Tabu Search Approach for 2D Strip Packing

Modeling, Analysis, and Applications in Metaheuristic Computing ◽

10.4018/978-1-4666-0270-0.ch011 ◽

2012 ◽

pp. 171-188

Author(s):

Giglia Gómez-Villouta ◽

Jean-Philippe Hamiez ◽

Jin-Kao Hao

Keyword(s):

Tabu Search ◽

Search Algorithm ◽

Fitness Function ◽

Packing Problem ◽

Two Dimensional ◽

Strip Packing ◽

Benchmark Instances ◽

Finite Set ◽

Infinite Height ◽

Search Approach

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

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Solving Multi-objective Two Dimensional Rectangle Packing Problem

Advances in Intelligent Systems and Computing - Proceedings of Sixth International Conference on Soft Computing for Problem Solving ◽

10.1007/978-981-10-3325-4_19 ◽

2017 ◽

pp. 188-196

Author(s):

Amandeep Kaur Virk ◽

Kawaljeet Singh

Keyword(s):

Packing Problem ◽

Two Dimensional ◽

Rectangle Packing ◽

Multi Objective ◽

Rectangle Packing Problem

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

Publications de l Institut Mathematique ◽

10.2298/pim1307095s ◽

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.

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