scholarly journals On Order-preserving, Gap-avoiding Rectangle Packing

2021 ◽  
Author(s):  
Sören Domrös ◽  
Daniel Lucas ◽  
Reinhard von Hanxleden ◽  
Klaus Jansen
Keyword(s):  
Rectangle Packing

An adaptive selection approach for the 2D rectangle packing area minimization problem

Omega ◽  
2018 ◽  
Vol 80 ◽  
pp. 22-30 ◽  
Author(s):  
Lijun Wei ◽  
Wenbin Zhu ◽  
Andrew Lim ◽  
Qiang Liu ◽  
Xin Chen
Keyword(s):  
Minimization Problem ◽  
Adaptive Selection ◽  
Rectangle Packing ◽  
Area Minimization ◽  
Selection Approach

Algorithms for Nesting of Ship/Offshore Structural Plates

1991 ◽  
Author(s):  
B. T. Cheok ◽  
A. Y. C. Nee
Keyword(s):  
Feature Extraction ◽  
Search Time ◽  
Computer Search ◽  
Rectangle Packing ◽  
Manual Method ◽  
Input And Output ◽  
Material Usage ◽  
Shape Processing ◽  
Cad Cam ◽  
Cam Systems

Abstract This paper discusses the development of a set of algorithms for the automatic nesting of ship/offshore structural plates. The algorithms are developed to take advantage of the peculiarity of most ship/offshore structural plates with the aims of optimising material usage and minimising computer search time. The parts to be nested are first processed by a shape processing routine which employs a simple feature extraction approach to classify the plates according to predefined rules specially adopted for ship/offshore structural shapes. The most appropriate search path for each class of plates is used to obtain the best enclosing rectangle for similar shapes. The search paths are based on heuristics developed to simulate the manual method used by the human operator. Finally, all the plates are laid out on the stock sheet using a “rectangle packing” approach. A computer package, Patnest-Ship was developed to demonstrate the efficiency of the algorithms and very encouraging results are achieved. The input and output files to and from Patnest-Ship are described in DXF format so that it can be integrated with existing CAD/CAM systems. Pre- and post-processors for this package have been implemented on AutoCAD to permit the user to define the plates and interactively improve on the solutions provided by Patnest-Ship, if necessary.

scholarly journals The Maximum of a Random Walk and Its Application to Rectangle Packing

1998 ◽  
Vol 12 (3) ◽  
pp. 373-386 ◽  
Author(s):  
E. G. Coffman ◽  
Philippe Flajolet ◽  
Leopold Flatto ◽  
Micha Hofri
Keyword(s):  
Random Walk ◽  
Upper Bound ◽  
Symmetric Random Walk ◽  
Rectangle Packing ◽  
Unit Width ◽  
Minimum Height ◽  
Image Position

Let S0,…,Sn be a symmetric random walk that starts at the origin (S0 = 0) and takes steps uniformly distributed on [— 1,+1]. We study the large-n behavior of the expected maximum excursion and prove the estimate,where c = 0.297952.... This estimate applies to the problem of packing n rectangles into a unit-width strip; in particular, it makes much more precise the known upper bound on the expected minimum height, O(n½), when the rectangle sides are 2n independent uniform random draws from [0,1].

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