Geração de padrões de cortes bidimensionais guilhotinados restritos via programação dinâmica e busca em grafo-e/ou

Morábito, Reinaldo; Pureza, Vitória

doi:10.1590/s0103-65132007000100003

Cited by 3 publications

(1 citation statement)

References 22 publications

(16 reference statements)

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“…The following comparison methods were included altogether for the first four instance sets: Beasley (2004) (in brief: B04 ), Alvarez‐Valdes et al (2005) ( APT05 ), Gonçalves and Resende (2006) ( GR06 ), Hadjiconstantinou and Iori (2007) ( HI07 ) and Alvarez‐Valdes et al (2007) ( APT07 ). For the fifth instances set, the following methods are used for a comparison: Fayard et al (1998) ( FHZ98 ), Alvarez‐Valdes et al (2002) ( APT02 ) and Morabito and Pureza (2007) ( MP07 ). For instances set Set6 the GA is only compared with the method from Fayard et al (1998) ( FHZ98 ).…”

Section: Testing the Methodsmentioning

confidence: 99%

A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces

Bortfeldt¹,

Winter²

2009

Int Trans Operational Res

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Given a set of rectangular pieces and a rectangular container, the two‐dimensional knapsack problem (2D‐KP) consists of orthogonally packing a subset of the pieces within the container such that the sum of the values of the packed pieces is maximized. If the value of a piece is given by its area, the objective is to maximize the covered area of the container. A genetic algorithm (GA) is proposed addressing the guillotine case of the 2D‐KP as well as the non‐guillotine case. Moreover, an orientation constraint may optionally be taken into account and the given piece set may be constrained or unconstrained. The GA is subjected to an extensive test using well‐known benchmark instances. Compared with recently published methods, the GA yields competitive results.

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Section: Testing the Methodsmentioning

confidence: 99%

A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces

Bortfeldt¹,

Winter²

2009

Int Trans Operational Res

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show abstract

A reduction approach for solving the rectangle packing area minimization problem

Bortfeldt

2013

European Journal of Operational Research

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Heurísticas para os problemas de geração e sequenciamento de padrões de corte bidimensionais

2007

Self Cite

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ResumoNeste artigo é tratado o clássico problema de corte de estoque bidimensional, cuja solução consiste em um conjunto de padrões de corte que otimiza uma função objetivo, por exemplo, a perda de material. Porém, os padrões de corte podem ser seqüenciados de modo que um outro objetivo também seja otimizado, como, por exemplo, o número máximo de pilhas abertas de itens (uma pilha é aberta quando um tipo de item é cortado pela primeira vez e fechada quando todos os itens deste tipo foram cortados). Uma boa solução para o problema de geração de padrões de corte freqüentemente não resulta numa boa solução para o problema de sequenciamento de padrões de corte, e vice-versa. Em geral, esses dois problemas são abordados, tanto na prática como na literatura, de forma independente e sucessiva. Pileggi et al. (2005) propuseram abordagens heurísticas para resolver esses dois problemas de forma integrada, considerando o trade-off entre os objetivos envolvidos, e analisaram o caso de corte unidimensional (p.e., corte de barras). No presente trabalho estas abordagens são estendidas e aplicadas para analisar o caso de corte bidimensional guilhotinado (p.e., corte de chapas). Resultados computacionais são apresentados para exemplos gerados aleatoriamente e para um exemplo real de uma fábrica de móveis.Palavras-chave: problema de corte bidimensional, sequenciamento de padrões de corte, heurísticas, otimização bi-objetivo. AbstractThis paper is concerned with the classical two-dimensional cutting stock problem, whose solution consists of a set of cutting patterns that optimize an objective function, for example, the waste of material. Nevertheless, the cutting patterns have to be sequenced so that another criterion is also optimized, for example, the maximum number of open stacks of the items (a stack is opened when a type of item is cut for the first time and closed when all items of this type were cut). A good solution for the problem of generating cutting patterns often does not result in a good solution for the problem of sequencing cutting patterns, and vice-versa. In general, these two problems are treated, either in practice or in the literature, in an independent and successive way. Pileggi et al. (2005) proposed heuristic approaches to solve these two problems in an integrated way, considering the trade-off between the objectives involved, and they analyzed the one-dimensional cutting case (e.g., cut of bars). In the present study these approaches are extended and applied to analyze the two-dimensional guillotine cutting case (e.g., cut of plates). Computational results are presented for randomly generated examples and for an actual instance of a furniture company.

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Geração de padrões de cortes bidimensionais guilhotinados restritos via programação dinâmica e busca em grafo-e/ou

Cited by 3 publications

References 22 publications

A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces

A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces

A reduction approach for solving the rectangle packing area minimization problem

Heurísticas para os problemas de geração e sequenciamento de padrões de corte bidimensionais

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