Nesting Problem of Irregular Shape Based on Motion Simulation

2020 ◽  
Vol 36 (02) ◽  
pp. 115-122
Author(s):  
Peiyong Li ◽  
Xiang Gao ◽  
Xiaodong Wu ◽  
HuaWei Zhang ◽  
Chong Wang
Keyword(s):  
Operations Research ◽  
Combinatorial Problem ◽  
New Method ◽  
Motion Simulation ◽  
Cutting And Packing ◽  
Shipbuilding Industry ◽  
Packing Problems ◽  
Running Time ◽  
Irregular Shapes ◽  
Nesting Problem

This article discusses cutting and packing problems found in the shipbuilding industry, with the aim of minimizing material wastage. The irregular nesting problem is a variation of such problems in which the container has variable length and fixed width. Nesting of irregular shapes is a combinatorial problem with nondeterministic polynomial complete difficulty. Generally, work on solving such problems is mainly conducted in the fields of geometry and operations research. This study proposes a new method for solving the nesting problem; i.e., shape nesting can be simulated by the motion of discrete bodies in a container with a fixed width. Calculation with the program developed by the authors has been performed, and the results show that the algorithm was able to achieve good compaction for the datasets, and the running time and utility of sheet are satisfied. Results of this study show that the new method based on motion simulation can be a new solution to the shape nesting problem.

scholarly journals TreeMerge: a new method for improving the scalability of species tree estimation methods

2019 ◽  
Vol 35 (14) ◽  
pp. i417-i426 ◽  
Author(s):  
Erin K Molloy ◽  
Tandy Warnow
Keyword(s):  
Large Scale ◽  
Species Tree ◽  
New Method ◽  
Divide And Conquer ◽  
Supplementary Information ◽  
Estimation Methods ◽  
Running Time ◽  
Tree Estimation ◽  
Computationally Intensive ◽  
A Minor

Abstract Motivation At RECOMB-CG 2018, we presented NJMerge and showed that it could be used within a divide-and-conquer framework to scale computationally intensive methods for species tree estimation to larger datasets. However, NJMerge has two significant limitations: it can fail to return a tree and, when used within the proposed divide-and-conquer framework, has O(n5) running time for datasets with n species. Results Here we present a new method called ‘TreeMerge’ that improves on NJMerge in two ways: it is guaranteed to return a tree and it has dramatically faster running time within the same divide-and-conquer framework—only O(n2) time. We use a simulation study to evaluate TreeMerge in the context of multi-locus species tree estimation with two leading methods, ASTRAL-III and RAxML. We find that the divide-and-conquer framework using TreeMerge has a minor impact on species tree accuracy, dramatically reduces running time, and enables both ASTRAL-III and RAxML to complete on datasets (that they would otherwise fail on), when given 64 GB of memory and 48 h maximum running time. Thus, TreeMerge is a step toward a larger vision of enabling researchers with limited computational resources to perform large-scale species tree estimation, which we call Phylogenomics for All. Availability and implementation TreeMerge is publicly available on Github (http://github.com/ekmolloy/treemerge). Supplementary information Supplementary data are available at Bioinformatics online.

Raster-based mathematical morphology for cutting and packing problems

2021 ◽  
Author(s):  
Fernanda Miyuki Yamada ◽  
Hiroki Takahashi ◽  
Harlen Costa Batagelo ◽  
João Paulo Gois
Keyword(s):  
Mathematical Morphology ◽  
Cutting And Packing ◽  
Packing Problems

scholarly journals A survey on the cutting and packing problems

2020 ◽  
Vol 13 (4) ◽  
pp. 567-572
Author(s):  
Loris Faina
Keyword(s):  
Three Dimensional ◽  
Cutting And Packing ◽  
Unified Approach ◽  
Geometrical Method ◽  
Packing Problems ◽  
Enumeration Scheme

Abstract This paper presents a unified approach, based on a geometrical method (see Faina in Eur J Oper Res 114:542–556, 1999; Eur J Oper Res 126:340–354, 2000), which reduces the general two and three dimensional cutting and packing type problems to a finite enumeration scheme.

An Adaptive Memetic Algorithm for Packing Problems of Irregular Shapes

2011 ◽  
Vol 314-316 ◽  
pp. 1029-1033
Author(s):  
Yu Yu Zhou ◽  
Yun Qing Rao ◽  
Guo Jun Zhang ◽  
Chao Yong Zhang
Keyword(s):  
Local Search ◽  
Memetic Algorithm ◽  
Raw Materials ◽  
Packing Problem ◽  
Search Method ◽  
Utilization Efficiency ◽  
Furniture Industry ◽  
Packing Problems ◽  
Irregular Shapes ◽  
Material Utilization

Packing problem, which occurs frequently in sheet metal, clothing and furniture industry, cut product patterns from raw materials most efficiently and maximize material utilization. In this paper, an adaptive memetic algorithm is proposed to solve the problem of irregular shapes packed on the rectangular sheets. First, operators and parameters of evolution is researched, and second, local search method is proposed. Finally, this study compares benchmarks presented by other authors. The results show that the material utilization efficiency by using the adaptive memetic algorithm is higher compared to other methods.

scholarly journals Algorithms for Working with Orthogonal Polyhedrons in Solving Cutting and Packing Problems

2021 ◽  
Author(s):  
Vladislav Chekanin ◽  
Alexander Chekanin
Keyword(s):  
Complex Shape ◽  
Three Dimensional ◽  
Geometric Transformation ◽  
Cutting And Packing ◽  
Packing Problems ◽  
Basic Model ◽  
Composite Objects ◽  
Hard Problems ◽  
Orthogonal Polyhedron ◽  
Polygonal Model

In this paper problems of cutting and packing objects of complex geometric shapes are considered. To solve these NP-hard problems, it is proposed to use an approach based on geometric transformation of polygonal objects to composite objects (orthogonal polyhedrons) made up of rectangles or parallelepipeds of a given dimension. To describe the free space inside a voxelized container, a model of potential containers is used as the basic model that provides the ability of packing orthogonal polyhedrons. A number of specialized algorithms are developed to work with orthogonal polyhedrons including: algorithms for placing and removing composite objects, an algorithm for forming a packing with a given distance between objects to be placed. Two algorithms for the placement of orthogonal polyhedrons are developed and their efficiency is investigated. An algorithm for obtaining a container of complex shape presented as an orthogonal polyhedron based on a polygonal model is given. The article contains examples of placement schemes obtained by the developed algorithms for solving problems of packing two-dimensional and three-dimensional non-rectangular composite objects.

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