Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing

Queiroz, Thiago Alves de; Miyazawa, Flávio Keidi; Wakabayashi, Yoshiko; Xavier, Eduardo C.

doi:10.1016/j.cor.2011.03.011

Cited by 43 publications

(11 citation statements)

References 23 publications

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“…Para calcular os raster points usamos o algoritmo RRP apresentado em [3]. Primeiro são gerados os pontos de discretização por um algoritmo de programação dinâmica, que consome tempo pseudo-polinomial, descrito em [19].…”

Section: A Rotina De Empacotamentounclassified

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Approaches for the 2D 0-1 knapsack problem with conflict graphs

Queiroz¹,

Miyazawa

2013

2013 XXXIX Latin American Computing Conference (CLEI)

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This work deals with the 0-1 knapsack problem in its two-dimensional variant, when there is a conflict graph related to pairs of conflicting items. Conflicting items must not be packed together in a same bin. This problem also arises as a subproblem in the bin packing problem and in supply chain scenarious. We propose a heuristic that generates iteratively a solution using a so called greedy randomized procedure. In order to avoid local optima solutions, a penalization memory list is used, and several packing strategies under a two-dimensional grid of points are considered. The heuristic solutions are compared with those ones computed by means of an integer programming model, also proposed in this work and solved with CPLEX solver. The heuristic got optimal solutions for 75% of the instances in a lower CPU time compared with that to solve the integer model.Keywords-Two-dimensional 0-1 knapsack problem, conflict graph, heuristic, integer programming. I. INTRODUÇÃOO problema da mochila 0-1é um clássico problema de otimização combinatória e aparece em diversos contextos práticos, bem como um subproblema de outros problemas de otimização, por exemplo, no problema de empacotamento em bins [1]. Variantes deste problema também têm sido apresentadas na literatura e aparecem nos meios práticos, como no caso bidimensional (2D): empacotamento de paletes e corte de chapas [2]; e no caso tridimensional (3D): empacotamento em contêineres [3]. Vale ressaltar que o problema da mochila 0-1 e suas variantes em outras dimensões são NP-difíceis [4].Uma restrição no problema da mochila 0-1 envolve itens conflitantes, ou seja, itens que não podem ser empacotados em um mesmo recipiente (por exemplo, por questões tecnológicas como alimentos e produtos tóxicos) [5], [6]. Neste caso, devese escolher qual dos itens empacotar no recipiente, gerando um empacotamento sem itens conflitantes.Este trabalho investiga o problema da mochila 0-1 na sua variante 2D considerando um grafo de conflitos associado aos itens. Este grafo mantém arestas entre itens conflitantes de forma que no máximo um deles esteja empacotado no recipiente. Os itens são elementos retangulares com largura e comprimento definidos, bem como um valor/lucro associado. O recipiente tambémé retangular e tem dimensões previamente definidas. O objetivoé empacotar em umúnico recipiente um subconjunto não-conflitante de itens que maximize o lucro total. O empacotamento final deve obedecer as dimensões do recipiente e os itens devem ser empacotados de forma ortogonal aos lados do recipiente, não podem se sobrepor e nem serem rotacionados. Denominaremos este problema por 2KPC. A. Trabalhos CorrelatosA versão unidimensional do problema da mochila 0-1 com grafo de conflitos foi inicialmente estudada por Yamada et al.[5], [6]. Tais autores apresentaram estratégias gulosas e algoritmos exatos para o problema. A estratégia principal gera uma solução inicial por meio de uma heurística gulosa, sendo melhorada por um processo de busca em vizinhança. As soluções são usadas como limitantes para o...

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Section: A Rotina De Empacotamentounclassified

“…Variantes deste problema também têm sido apresentadas na literatura e aparecem nos meios práticos, como no caso bidimensional (2D): empacotamento de paletes e corte de chapas [2]; e no caso tridimensional (3D): empacotamento em contêineres [3]. Vale ressaltar que o problema da mochila 0-1 e suas variantes em outras dimensões são NP-difíceis [4].…”

Section: Introductionunclassified

Approaches for the 2D 0-1 knapsack problem with conflict graphs

Queiroz¹,

Miyazawa

2013

2013 XXXIX Latin American Computing Conference (CLEI)

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“…the bins and boxes are available at a certain date. C&P problems have been addressed by searching heuristics such as tabusearch [1,5], ACO [8] or branch-and-bound techniques [9], by simpler heuristics [4,10] or by mixed integer programming methods using column-approach [11]. However, the last ones are often applied to simpler cases, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…However, the last ones are often applied to simpler cases, i.e. less heterogeneous set of boxes with single bin cases [11] or two-dimensional cases [7] among other features that reduce the number of possible cutting patterns, due to the computational burden [2]. In this way, as the addressed problem is one of the most complex type of problems found in the literature, this study focuses on heuristics and metaheuristics.…”

Section: Introductionmentioning

confidence: 99%

An ACO Algorithm for the 3D Bin Packing Problem in the Steel Industry

Silveira

Vieira

Sousa

2013

Recent Trends in Applied Artificial Intelligence

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Abstract. This paper proposes a new Ant Colony Optimization (ACO) algorithm for the three-dimensional (3D) bin packing problem with guillotine cut constraint, which consists of packing a set of boxes into a 3D set of bins of variable dimensions. The algorithm is applied to a realworld problem in the steel industry. The retail steel cut consists on how to cut blocks of steel in order to satisfy the clients orders. The goal is to minimize the amount of scrap metal and consequently reduce the stock of steel blocks. The proposed ACO algorithm searches for the best orders of the boxes and it is guided by a heuristic that determines the position and orientation for the boxes. It was possible to reduce the amount of scrap metal by 90% and to reduce the usage of raw material by 25%.

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“…The geometry-dependent problem solving involves selection of elements (resources), dimensions of shapes (1D, 2D, 3D, or nD), and its representation [5,[8][9][10]:  1D (one-dimensional shapes): bars [11];  2D (two-dimensional shapes): rectangles, trapezoids, circles, convex, concave and irregular shapes [7,[12][13][14][15][16][17][18];  3D (three-dimensional shapes) [19,20];  nD (n-dimensional shapes) [21,22].…”

Section: Introductionmentioning

confidence: 99%

A Universal CAD System for Cutting Stock Problem

Kovačić¹,

Brezočnik²

2017

Int. j. simul. model.

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In this research the universal system using CAD geometry for solving of cutting stock problem is proposed. The system consists of the three main modules: geometry definition module, objective definition module, and the search strategy module. In the first module the reference points and orientation of parts and stock are defined. In the second module some constraints such as the quantity of the desired type of parts to be placed on the stock can be taken into account. The third module contains the search strategy. For the purpose of this research, the genetic algorithm was used as the search method. For illustration of the generality of the proposed approach, three practical examples for solving orthogonally and irregularly-shaped cutting stock problems are presented. The parts which are to be cut from stock-material with minimal loss and also the stock-material itself are presented as CAD geometries without any kind of geometrical constraints (i.e., concavity, convexity, sections, and holes). In the presented approach the AutoCAD environment was used. The AutoLISP in-house developed system for cutting stock problem was integrated into the AutoCAD. The developed system is without any kind of geometrical constraints and thus highly applicable in the practice. The presented approach can be developed also in other CAD systems where the application programming interfaces (API) are available.

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Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing

Cited by 43 publications

References 23 publications

Approaches for the 2D 0-1 knapsack problem with conflict graphs

Approaches for the 2D 0-1 knapsack problem with conflict graphs

An ACO Algorithm for the 3D Bin Packing Problem in the Steel Industry

A Universal CAD System for Cutting Stock Problem

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