On a Genetic-Tabu Search Based Algorithm for Two-Dimensional Guillotine Cutting Problems

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infinite height. Finally, they undertake an extensive experimental study with a large number of problem instances extracted from the literature by the Hopper’s benchmarks in order to support and to prove their approach and to evaluate the performance. DOI: 10.4018/japuc.2012040103 International Journal of Advanced Pervasive and Ubiquitous Computing, 4(2), 26-40, April-June 2012 27 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. problems, 2D rectangular strip packing (even with these restrictions) is NP-hard. Finally, our algorithm naturally solves a more general problem: given a set of rectangles and a target rectangle, find a packing of a subset of those rectangles which gives an optimal packing of the target. Numerical examples also showed the superiority of the proposed algorithm compared with two classical methods in the literature (pure genetic algorithm and hopper’s results) (Hopper & Turton, 2002). This paper is organized as follows. In the following section, we provide the problem description and the literature review. After, we present the resolution methods which use the bottom left algorithm and the guillotine constraint. In the fourth section, we show how our hybrid algorithm can be adapted for solving the general 2DC problem. Then, we undertake a comparative study of our proposed algorithm and evaluate its performance for the 2DC problem using benchmark problems from the literature. Finally, we summarize the contributions of this paper and explain its possible extensions. A BRIEF STATE OF THE ART Because of its importance and despite its NPhardness, the Two Dimensional Cutting (TDC) problem has been widely studied in the literature. Indeed, there are three key components of the problem under consideration; bin packing, guillotine cuts and regular shapes (rectangular form). To our knowledge there are no papers that tackle these three together with a hybrid genetic algorithm. In addition, regular shape packing literature is almost exclusively strip packing; one infinite length stock sheet, and a finite fixed set of rotation angles. In this paper all pieces are regular with a rectangular form; instead the key challenge arises in modeling efficiently continuous rotation of the pieces, which is not commonly dealt with in the literature. The rectangle bin packing problem with guillotine constraints has the most similarities to the problem we are tacking in this paper. Lodi, Martello, and Monaci (2002), survey two dimensional rectangle bin packing, including algorithms that handle guillotine constraints. They describe the oneand two-phase approach; both consist of packing pieces onto shelves along the width of the bin, the former directly packing into the bin, the latter also optimizes how the shelves are packed into the bins; analogous to a one dimensional bin packing problem. Lodi et al. (1999) create the shelves by solving a series of 0-1 knapsack problems improving on the performance of the finite first fit and finite best strip heuristics of Berkey and Wang (1987). More recent construction heuristics are not constrained to creating shelves. Charalambous and Fleszar (2011) start by generating simple patterns, initially across the width of the bin, and subsequently within free rectangle areas. Pieces may shift horizontally or vertically in order to maximize the size of the free rectangle, while maintaining the guillotine constraint. Polyakovsky and MHallah (2009) modify the well know bottom left construction heuristic to meet guillotine constraints. After placing each piece, they apply both horizontal and vertical guillotine cuts and select the one that gives the largest rectangle area available for packing. Pieces are assigned to bins using an agent-based algorithm. Pieces may be agentinitiators attracting individual-agents (pieces) to their group in order to maximize the fitness of the group. Individual-agents compete to join groups to maximize their purpose parameters. These groups are assigned to the same bin and arranged using the guillotine bottom left heuristic. Initially, one piece is packed in each bin. The heuristic attempts to empty weak bins by assigning pieces to sub-instances that include the pieces from k bins. Instead of assigning pieces to bins and then packing, Alvelos, Chan, Vilaca, Silva, and Valerio de Carvalho (2009) define a sequence for packing the pieces while keeping a list of candidate locations for the next piece. The solution is improved using variable neighborhood descent where moves are made within the packing sequence. Although none of these papers directly apply to the problem addressed in this paper, we have made use of 13 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/genetic-tabu-search-basedalgorithm/71883?camid=4v1 This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Communications and Social Science. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2