Main.CircleChallenge History

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April 15, 2013, at 08:36 AM by 98.197.65.68 -
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Thanks to Frank Kampas for providing source code and animations for this challenge problem. Frank holds a Ph.D. in physics from Stanford University and can be reached at frank@physicistatlarge.com.
April 13, 2013, at 10:17 PM by 69.169.188.188 -
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April 12, 2013, at 10:20 PM by 69.169.188.188 -
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April 12, 2013, at 10:19 PM by 69.169.188.188 -
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April 12, 2013, at 10:19 PM by 69.169.188.188 -
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Attach:10_circle_packing_anim.gif
March 28, 2013, at 09:37 AM by 128.187.97.24 -
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February 25, 2013, at 02:52 PM by 128.187.97.21 -
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!!!! Download Sample MATLAB Code

MATLAB source code writes an APM optimization file and sends it to the APMonitor server for solution. After the script executes, a figure appears that shows the best and worst configurations.

* [[Attach:CirclePacking_MATLAB.zip|MATLAB Example Source Code]]
[[Attach:CirclePacking_MATLAB.zip|Attach:CirclePacking_MATLAB.png]]
February 19, 2013, at 07:29 AM by 69.169.188.188 -
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* [[http://apmonitor.com/online/view_pass.php?f=circlepack4.apm|Solve 4 Circle Packing Problem]]
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* [[http://apmonitor.com/online/view_pass.php?f=circlepack4.apm|Solve 4 Circle Packing Problem Online]]
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* [[http://apmonitor.com/online/view_pass.php?f=circlepack10.apm|Solve 10 Circle Packing Problem]]

(:html:)
<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles10.htm" width="500" height="1500" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
(:htmlend:)
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* [[http://apmonitor.com/online/view_pass.php?f=circlepack10.apm|Solve 10 Circle Packing Problem Online]]
February 19, 2013, at 07:26 AM by 69.169.188.188 -
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* [[Attach:CirclePacking_v2.zip|Python Example Source Code for 10 Circles]]
[[Attach:CirclePacking_v2.zip|Attach:CirclePacking10.png]]
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* [[Attach:CirclePacking_v2.zip|Python Example Source Code for Multi-Start]]
[[Attach:CirclePacking_v2.zip|Attach:CirclePacking_multi.png]]
February 19, 2013, at 07:20 AM by 69.169.188.188 -
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!!!! Download Sample Python Code
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!!!! Download Sample Python Code - Version 1
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(:htmlend:)

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!!!! Download Sample Python Code - Version 2

A second version solves multiple circle packing optimization problems with the same model using multi-dimensional arrays. Python source code re-writes the optimization file and sends it to the APM server for solution. After the script executes, a figure appears that shows the configuration that was produced.

* [[Attach:CirclePacking_v2.zip|Python Example Source Code for 10 Circles]]
[[Attach:CirclePacking_v2.zip|Attach:CirclePacking10.png]]

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!!!! Example Solution for 10 Circles

Attach:10_circle_packing.png

* [[http://apmonitor.com/online/view_pass.php?f=circlepack10.apm|Solve 10 Circle Packing Problem]]

(:html:)
<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles10.htm" width="500" height="1500" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
February 15, 2013, at 09:17 PM by 69.169.131.173 -
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February 15, 2013, at 09:14 PM by 69.169.131.173 -
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* 'containers' - in this case a circle that circuscribes all of the other circles
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* 'containers' - in this case a circle that circumscribes all of the other circles
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Python source code re-writes the optimization file and sends it to the APM server for solution. After the script executes, a figure appears that shows the configuration that was produced.
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* [[http://apmonitor.com/online/view_pass.php?f=circlepack4.apm|Solve 4 Circle Packing Problem]]
February 15, 2013, at 06:03 PM by 128.187.97.21 -
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<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles.htm" width="450" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
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<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles.htm" width="500" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
February 15, 2013, at 06:02 PM by 128.187.97.21 -
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<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles.htm" width="550" height="700" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
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<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles.htm" width="450" height="600" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
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<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="400" height="600" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
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<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="550" height="900" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
February 15, 2013, at 06:02 PM by 128.187.97.21 -
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<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="500" height="800" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
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<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="400" height="600" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
February 15, 2013, at 06:01 PM by 128.187.97.21 -
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<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="550" height="1000" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
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<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="500" height="800" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
February 15, 2013, at 06:00 PM by 128.187.97.21 -
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(:html:)
<iframe src="http://apmonitor.com/me575/uploads/Main/packcircles.htm" width="550" height="700" frameborder="1" marginheight="0" marginwidth="0">Loading...</iframe>
(:htmlend:)
February 15, 2013, at 05:54 PM by 128.187.97.21 -
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February 15, 2013, at 05:54 PM by 128.187.97.21 -
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!!!! Background

Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together (often inside a container), as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues. In a packing problem, you are given:

* 'containers' - in this case a circle that circuscribes all of the other circles
* 'goods' (usually a single type of shape), some or all of which must be packed into this container

Usually the packing must be without overlaps between goods and other goods or the container walls. The aim is to find the configuration with the maximal density. In some variants the overlapping (of goods with each other and/or with the boundary of the container) is allowed but should be minimized.
February 15, 2013, at 05:32 PM by 128.187.97.21 -
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!!!! Example Solution for 4 Circles

Attach:4_circle_packing.png
February 15, 2013, at 05:29 PM by 128.187.97.21 -
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* [[Attach:CirclePacking.zip|Python Example Source Code]]
[[Attach:CirclePacking.zip|Attach:CirclePacking.png]]
February 15, 2013, at 05:15 PM by 128.187.97.21 -
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(:title Circle Packing Challenge Activity:)
(:keywords project, nonlinear, optimization, engineering optimization, engineering design, interior point, active set, circle packing, packing optimization, python, matlab:)
(:description A challenge problem to determine the minimum circumscribing radius for n circles with radius i^(-0.5) for i=1..n.:)

!!!! Challenge Problem in Global Optimization

Determine the minimum circumscribing radius for n circles with radius i^(-0.5) for i=1..n.

!!!! Download Sample Python Code



!!!! Record Your Best Answer

(:html:)
<iframe src="https://docs.google.com/a/apmonitor.com/spreadsheet/embeddedform?formkey=dGp4bExwUU1wOVhOT3M1T2otY1g3LXc6MQ" width="550" height="1000" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
(:htmlend:)


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(:html:)
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