A clique covering MIP model for the irregular strip packing problem

Rodrigues, Marcos Okamura; Toledo, Franklina Maria Bragion de

doi:10.1016/j.cor.2016.11.006

Cited by 28 publications

(19 citation statements)

References 34 publications

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“…These approaches compute a solution by solving certain mathematical models for the packing problems. These proposed models include the mixedinteger programming (MIP) model with a linear objective function and mixed-integer constraints [2], [15], [22], [32], [40], [42], nonlinear programming models with a nonlinear objective function [14], [15], [29], [30], [44], and constraintbased programming models where the packing problem is described by constraints [12], [38], [39]. Interested readers are referred to the references in the survey [33].…”

Section: Introductionmentioning

confidence: 99%

Greedy Adaptive Search: A New Approach for Large-Scale Irregular Packing Problems in the Fabric Industry

Cui

2020

IEEE Access

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The 2-dimensional irregular packing problems are important in the fabric industry. Under several restrictions, fabric packing problems require placing a given set of parts within a fixed-width rectangular sheet, aiming at a minimum length use. In textile industry production, the fabric packing problems are usually large-scale with time limits, where the total number of parts is large, and a highutilization solution should be computed in several minutes. However, there are few existing works on largescale packing problems. In this paper, we propose a greedy adaptive search algorithm by constructing a new evaluation function and introducing a new restricted local search strategy. In our algorithm, with a given initial sequence of parts, we iteratively search the best-fit part in succeeding several parts and place it on sheet. Moreover, we employ a two-stage heuristic searching algorithm to search over all the possible sequences for a good initial sequence with high utilization. Numerical examples involve some large-scale industrial instances, together with some large-scale instances generated from benchmarks. Numerical tests show that our algorithm outperforms existing state-of-the-art solvers in large-scale packing problems. The results show the potential of our algorithm to large-scale packing problems in industrial production.

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Section: Introductionmentioning

confidence: 99%

Greedy Adaptive Search: A New Approach for Large-Scale Irregular Packing Problems in the Fabric Industry

Cui

2020

IEEE Access

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“…Their model builds on the linear programming compaction approaches (for example Bennell and Downsland (2001)) and adds binary variables to activate and deactivate constraints. Larger problems are solved by Rodrigues and Toledo (2017) where their integer programming model approximates the stock sheet by discrete points. A compromise between the two approaches is proposed by Leao et al (2016) who discretise the stock sheet in the y-axis but allow continuous translations in the x-direction.…”

Section: Introductionmentioning

confidence: 99%

A beam search approach to solve the convex irregular bin packing problem with guillotine cuts

Bennell

Cabo

Martínez-Sykora

2018

European Journal of Operational Research

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This paper presents a two dimensional convex irregular bin packing problem with guillotine cuts. The problem combines the challenges of tackling the complexity of packing irregular pieces, guaranteeing guillotine cuts that are not always orthogonal to the edges of the bin, and allocating pieces to bins that are not necessarily of the same size. This problem is known as a two-dimensional multi bin size bin packing problem with convexirregular pieces and guillotine cuts. Since pieces are separated by means of guillotine cuts, our study is restricted to convex pieces. A beam search algorithm is described, which is successfully applied to both the multi and single bin size instances. The algorithm is competitive with the results reported in the literature for the single bin size problem and provides the first results for the multi bin size problem.

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“…De acordo com [9], o problema de empacotamento de peças irregularesé NP-completo. Isso justifica o atual cenário daárea, onde há um grande número de artigos que utilizam heurísticas e/ou meta-heurísticas para tratar o problema [3], enquanto poucos métodos exatos são propostos [1,4,5,8,12,18,20].…”

Section: Introductionunclassified

Modelo integrado de empacotamento de peças irregulares em faixa e caminho mínimo de corte

Oliveira¹,

Silva²,

Toledo³

et al. 2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. O problema de empacotamento de peças irregulares em faixas visa definir um plano de corte de peças irregulares a serem cortadas a partir de placas maiores minimizando a perda de material utilizado. Em algumas indústrias surge, após a determinação do plano de corte, um segundo problema: a determinação do caminho mínimo de corte. Embora a solução do primeiro influencie fortemente a resolução do segundo, nãoé de nosso conhecimento que exista um modelo matemático que integre estes problemas. Neste artigo, propomos o primeiro modelo integrado de empacotamento de peças irregulares em faixa e de caminho mínimo de corte.Palavras-chave. Problema de empacotamento, caminho de corte, integração

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A clique covering MIP model for the irregular strip packing problem

Cited by 28 publications

References 34 publications

Greedy Adaptive Search: A New Approach for Large-Scale Irregular Packing Problems in the Fabric Industry

Greedy Adaptive Search: A New Approach for Large-Scale Irregular Packing Problems in the Fabric Industry

A beam search approach to solve the convex irregular bin packing problem with guillotine cuts

Modelo integrado de empacotamento de peças irregulares em faixa e caminho mínimo de corte

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