Mathematical model and efficient algorithms for object packing problem

Chernov, N.; Stoyan, Yu. G.; Romanova, Tatiana

doi:10.1016/j.comgeo.2009.12.003

Cited by 130 publications

(113 citation statements)

References 23 publications

(54 reference statements)

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“…The heuristic algorithms are also applicable to 3D packaging efficiency simulations (i.e., cargo shipments and granular media packaging). For the prescribed models, most are commonly used to analyze simplified polygons fixed in a specific orientation denoted as phi-objects [74]. Similar phi-object models are presented in [75,76].…”

Section: Areas Of Improvement and Comparison To Other Technologiesmentioning

confidence: 99%

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Laureto

Pearce

2017

Technologies

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Abstract:As low-cost desktop 3D printing is now dominated by free and open source self-replicating rapid prototype (RepRap) derivatives, there is an intense interest in extending the scope of potential applications to manufacturing. This study describes a manufacturing technology that enables a constrained set of polymer-metal composite components. This paper provides (1) free and open source hardware and (2) software for printing systems that achieves metal wire embedment into a polymer matrix 3D-printed part via a novel weaving and wrapping method using (3) OpenSCAD and parametric coding for customized g-code commands. Composite parts are evaluated from the technical viability of manufacturing and quality. The results show that utilizing a multi-polymer head system for multi-component manufacturing reduces manufacturing time and reduces the embodied energy of manufacturing. Finally, it is concluded that an open source software and hardware tool chain can provide low-cost industrial manufacturing of complex metal-polymer composite-based products.

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Section: Areas Of Improvement and Comparison To Other Technologiesmentioning

confidence: 99%

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Laureto

Pearce

2017

Technologies

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“…See Chernov et al (2010) for details of this procedure. These phi-functions are deconstructed into phi-trees where the terminal nodes correspond to systems of nonlinear inequalities, each focusing on a subset of configurations of the polygons.…”

Section: Clustering Approachmentioning

confidence: 99%

Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints

Han

Bennell

Zhao

et al. 2013

European Journal of Operational Research

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The paper examines a new problem in the irregular packing literature that has existed in industry for decades; two-dimensional irregular (convex) bin packing with guillotine constraints. Due to the cutting process of certain materials, cuts are restricted to extend from one edge of the stock-sheet to another, called guillotine cutting. This constraint is common place in glass cutting and is an important constraints in two-dimensional cutting and packing problems. In the literature, various exact and approximate algorithms exist for finding the two dimensional cutting patterns that satisfy the guillotine cutting constraint. However, to the best of our knowledge, all of the algorithms are designed for solving rectangular cutting where cuts are orthogonal with the edges of the stock-sheet. In order to satisfy the guillotine cutting constraint using these approaches, when the pieces are non-rectangular, practitioners implement a two stage approach. First, pieces are enclosed within rectangle shapes and then the rectangles are packed. Clearly, imposing this condition is likely to lead to additional waste. This paper aims to generate guillotine-cutting layouts of irregular shapes using a number of strategies. The investigation compares two two-stage approaches; one approximates pieces by rectangles, the other approximates pairs of pieces by rectangles using phi-functions for optimal clustering. Both these approaches use state of the art rectangle bin packing with guillotine constraints. Further, we design and implement a one-stage approach using a self-adapted forest search algorithm. Experimental results show the one-stage strategy to produce good solutions in less time over the two-stage approach.

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“…A tutorial covering the core geometric methodologies currently applied by researchers in cutting and packing of irregular shapes is presented by [4]. Tools of mathematical modeling of arbitrary object packing problems are given by [6,10,11]. Complexity investigations for cutting and packing problems can be found in [7,9,12,20] .…”

Section: Related Workmentioning

confidence: 99%

“…Each element i l is given by tuple ( , , , , ) Given the ordered collection of line segments and circular arcs, we apply the decomposition algorithm given in [10] to obtain a set of basic objects that describe the object.…”

Section: Placement Objectsmentioning

confidence: 99%

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Optimal clustering of a pair of irregular objects

Bennell¹,

Scheithauer

Stoyan

et al. 2014

J Glob Optim

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Abstract.Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects.

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Mathematical model and efficient algorithms for object packing problem

Cited by 130 publications

References 23 publications

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Open Source Multi-Head 3D Printer for Polymer-Metal Composite Component Manufacturing

Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints

Optimal clustering of a pair of irregular objects

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