Journal ArticleDOI
A generic approach for nesting of 2-D parts in 2-D sheets using genetic and heuristic algorithms
A. Ramesh Babu,N. Ramesh Babu +1 more
TLDR
A new method of representing the sheet and part geometries in discrete form to arrange the parts on the sheet quickly, irrespective of the complexity in the geometry of the sheets and parts is proposed.Abstract:
In this paper, a genetic and heuristic approach is proposed for the nesting of multiple two-dimensional (2-D) shaped parts in multiple 2-D shaped sheets with the aim of minimizing the wastage of the sheet material. The paper proposes a new method of representing the sheet and part geometries in discrete form to arrange the parts on the sheet quickly, irrespective of the complexity in the geometry of the sheets and parts. The proposed heuristic approach considers the sheets and parts in a sequential manner and arranges the parts on the sheets using the bottom-left strategy. The genetic algorithm generates the best sequence of the sheets and parts for nesting the parts on multiple sheets, utilizing the sheet material optimally. The effectiveness of the proposed approach is shown by comparing the results obtained with the present approach to those obtained with the approaches proposed by Jakobs (Eur J Oper Res, 88 (1996) 165), Ramesh Babu and Ramesh Babu (Int J Prod Res, 37(7) 1999 1625), and Jain and Chang (Engng Comput, 14 (1998) 206). The generic nature of the present approach is illustrated by considering a variety of parts, ranging from a simple rectangular shape to a highly irregular shape, in different combinations with or without grain orientation constraint, apart from nesting of multiple irregular shaped parts in multiple sheets of complex geometry.read more
Citations
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Journal ArticleDOI
The geometry of nesting problems: A tutorial
TL;DR: A tutorial covering the core geometric methodologies currently employed by researchers in cutting and packing of irregular shapes to equip new and current researchers in the area to select the most appropriate methodology for their needs is provided.
Journal ArticleDOI
A tutorial in irregular shape packing problems
TL;DR: The aim is not to give a chronological account or an exhaustive review, but to draw on the literature to describe and evaluate the core approaches to irregular shape packing.
Journal ArticleDOI
A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering
TL;DR: A methodology that hybridizes cuckoo search and guided local search optimization techniques is proposed, which aims to minimize the length of the sheet while having all polygons inside the sheet without overlap.
Journal ArticleDOI
A beam search implementation for the irregular shape packing problem
Julia A. Bennell,Xiang Song +1 more
TL;DR: This paper investigates the irregular shape packing problem as an ordered list of pieces to be packed where the order is decoded by a placement heuristic and implements a beam search algorithm to search over the packing order.
Journal ArticleDOI
A branch & bound algorithm for cutting and packing irregularly shaped pieces
TL;DR: An extensive computational study is made of the cutting and packing problems involving irregular shapes and an exact Branch & Bound Algorithm is developed, able to solve instances of up to 16 pieces to optimality.
References
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Book
Genetic algorithms in search, optimization, and machine learning
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Genetic algorithms in search, optimization and machine learning
TL;DR: This book brings together the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Book
Modern heuristic techniques for combinatorial problems
TL;DR: In this paper, the Lagrangian relaxation and dual ascent tree search were used to solve the graph bisection problem and the graph partition problem, and the traveling salesman problem scheduling problems.
Journal ArticleDOI
Adaptive probabilities of crossover and mutation in genetic algorithms
M. Srinivas,Lalit M. Patnaik +1 more
TL;DR: An efficient approach for multimodal function optimization using genetic algorithms (GAs) and the use of adaptive probabilities of crossover and mutation to realize the twin goals of maintaining diversity in the population and sustaining the, convergence capacity of the GA are described.
Journal ArticleDOI
On genetic algorithms for the packing of polygons
TL;DR: A genetic algorithm for placing polygons on a rectangular board is proposed and it is shown that the algorithm is improved by combination with deterministic methods.