NDLI: Packing circular-like objects in a rectangular container

Content Provider	Springer Nature Link
Author	Litvinchev, I. Infante, L. Ozuna, L.
Copyright Year	2015
Abstract	A problem of packing unequal circles in a fixed size rectangular container is considered. The aim is to maximize the (weighted) number of circles placed into the container or minimize the waste. The circle is considered in a general sense, as a set of points that are all the same distance (not necessary Euclidean) from a given point. An integer formulation is proposed using a grid approximating the container and considering the nodes of the grid as potential positions for assigning centers of the circles. The packing problem is then stated as a large scale linear 0–1 optimization problem. The binary variables represent the assignment of centers to the nodes of the grid. The resulting binary problem is then solved by commercial software. Valid inequalities are proposed to strengthening the original formulation. Nesting circles inside one another is considered tacking into account the thickness of the circles. Numerical results on packing circles, ellipses, rhombuses and octagons are presented to demonstrate the efficiency of the proposed approach.
Starting Page	259
Ending Page	267
Page Count	9
File Format	PDF
ISSN	10642307
Journal	Journal of Computer and Systems Sciences International
Volume Number	54
Issue Number	2
e-ISSN	15556530
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-04-12
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Control, Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computer Networks and Communications Control and Systems Engineering Information Systems Computer Vision and Pattern Recognition Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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