Towards an evolved lower bound for the most circular partition of a square

Claudia Obermaier; Markus Wagner

doi:10.1109/CEC.2009.4983115

Towards an evolved lower bound for the most circular partition of a square

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

We examine the problem of partitioning a square into convex polygons which are as circular as possible. Circular means that the polygon's aspect ratio is supposed to be near 1. The aspect ration of a convex polygon denotes the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. This problem has been solved for the equilateral triangle as well as for regular k-gon with k > 4. In the case of a square, the optimal solution is still an open problem. We are planning to find a solution which is "good enough" with the help of evolutionary algorithms.

Original language	English
Title of host publication	2009 IEEE Congress on Evolutionary Computation, CEC 2009
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	1463-1469
Number of pages	7
ISBN (Print)	9781424429592
DOIs	https://doi.org/10.1109/CEC.2009.4983115
Publication status	Published - 2009
Externally published	Yes
Event	IEEE Congress on Evolutionary Computation 2009 - Trondheim, Norway Duration: 18 May 2009 → 21 May 2009 https://ieeexplore.ieee.org/xpl/conhome/4939002/proceeding (Proceedings)

Conference

Conference	IEEE Congress on Evolutionary Computation 2009
Abbreviated title	CEC 2009
Country/Territory	Norway
City	Trondheim
Period	18/05/09 → 21/05/09
Internet address	https://ieeexplore.ieee.org/xpl/conhome/4939002/proceeding (Proceedings)

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10.1109/CEC.2009.4983115

Cite this

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title = "Towards an evolved lower bound for the most circular partition of a square",

abstract = "We examine the problem of partitioning a square into convex polygons which are as circular as possible. Circular means that the polygon's aspect ratio is supposed to be near 1. The aspect ration of a convex polygon denotes the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. This problem has been solved for the equilateral triangle as well as for regular k-gon with k > 4. In the case of a square, the optimal solution is still an open problem. We are planning to find a solution which is {"}good enough{"} with the help of evolutionary algorithms.",

author = "Claudia Obermaier and Markus Wagner",

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doi = "10.1109/CEC.2009.4983115",

language = "English",

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pages = "1463--1469",

booktitle = "2009 IEEE Congress on Evolutionary Computation, CEC 2009",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

address = "United States of America",

note = "IEEE Congress on Evolutionary Computation 2009, CEC 2009 ; Conference date: 18-05-2009 Through 21-05-2009",

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AU - Wagner, Markus

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AB - We examine the problem of partitioning a square into convex polygons which are as circular as possible. Circular means that the polygon's aspect ratio is supposed to be near 1. The aspect ration of a convex polygon denotes the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. This problem has been solved for the equilateral triangle as well as for regular k-gon with k > 4. In the case of a square, the optimal solution is still an open problem. We are planning to find a solution which is "good enough" with the help of evolutionary algorithms.

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DO - 10.1109/CEC.2009.4983115

M3 - Conference Paper

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SN - 9781424429592

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BT - 2009 IEEE Congress on Evolutionary Computation, CEC 2009

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T2 - IEEE Congress on Evolutionary Computation 2009

Y2 - 18 May 2009 through 21 May 2009

ER -

Towards an evolved lower bound for the most circular partition of a square

Abstract

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