A new heuristic algorithm for two-dimensional defective stock guillotine cutting stock problem with multiple stock sizes

Jin, Maozhu; Ge, Pen; Ren, Peiyu

doi:10.17559/tv-20150731113849

Cited by 4 publications

(8 citation statements)

References 17 publications

(18 reference statements)

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“…Scheithauer et al [23] solved the problem of guillotine cutting rectangle from rectangular and defective boards with dynamic programming. Jin et al [24] proposed a heuristic for solving the packing on defective rectangular plates. FSS algorithm was proposed by Beasley et al Genetic algorithm is a random global search and optimization method and has been effectively applied to solve various combinatorial optimization problems.…”

Section: Rectangle Packing Of Irregular Platesmentioning

confidence: 99%

Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

et al. 2020

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Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL) heuristic proposed in this paper to obtain feasible solutions, and then applies the genetic algorithm to optimize the quality of solutions further. The HL heuristic is constructed on the basis of computational geometry and level packing. This heuristic aims to divide the irregular plate into multiple subplates horizontally, calculates the movable positions of the rectangle in the subplates, determines whether or not the rectangle can be packed in the movable positions through computational geometry, and fills the scraps appropriately. Theoretical analysis confirms that the rectangles obtained through the HL heuristic are inside the plate and do not overlap with the defects. In addition, the packed rectangles do not overlap each other and satisfy the guillotine constraint. Accordingly, the packing problem can be solved. Experiments on irregular slates with defects show that the slate utilization through our method is between 89% and 95%. This result is better than manual packing and can satisfy actual production requirements.

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Section: Rectangle Packing Of Irregular Platesmentioning

confidence: 99%

Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

et al. 2020

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“…The result of the first stage is the cutting plan. In each suborder at most one leftover is larger than max(lihki) (8). The decision-maker decides about D and leftovers of all suborders larger than D can then be treated as UL and returned to stock and so the procedure can be completed.…”

Section: Solution Developmentmentioning

confidence: 99%

“…Algorithm for the cutting stock process by suborders in pseudo code Without constraint (8) in which only one leftover larger than max(l i h ki ) is allowed, optimised pairs could simply be gathered into suborders.…”

Section: Creation Of Suborders and Solution Of The 1dcspulmentioning

confidence: 99%

“…Examples range from the metal [3], paper [4], textile and wood industries [5] through to nanotechnology [6]. They face the same problem of how to cut ordered items out of what are generally different stock lengths to minimise the trim-loss [7] and maximize the utilization of stocks [8]. The trimloss is the leftovers of the cutting process that are too short to be used in subsequent orders and are treated as waste.…”

Section: Introductionmentioning

confidence: 99%

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One-Dimensional Cutting Stock Optimisation by Suborders

2018

Teh. vjesn.

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This paper introduces a method for solving a one-dimensional cutting stock problem by suborders. The method is used for large orders that for technological and logistical reasons cannot be filled in a single order, but only in several successive suborders. The method has two stages. In the first stage, the suborders are generated and in the second the trim-loss is minimised. All leftovers longer than D are returned to stock and reused. Shorter leftovers are treated as trim-loss and discarded. A detailed description of the method is provided by using a practical case. The method is tested by solving 108 randomly generated problem instances.

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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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A new heuristic algorithm for two-dimensional defective stock guillotine cutting stock problem with multiple stock sizes

Cited by 4 publications

References 17 publications

Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

One-Dimensional Cutting Stock Optimisation by Suborders

A Universal CAD System for Cutting Stock Problem

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