Box Folding Optimization
Main.BoxFolding History
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Test your knowledge with a [[https://apmonitor.com/pdc/index.php/Main/QuizSchedulingControl|Quiz on Box Folding Optimization]]
Deleted lines 50-68:
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Changed line 44 from:
m.Obj(Volume) # how to maximize Volume?
to:
m.Maximize(Volume)
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'''[[https://gekko.readthedocs.io/en/latest/|Python Gekko]] Solution'''
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(:source lang=python:)
from gekko import GEKKO
m = GEKKO()
tabs = 5.0 / 100 # m = cm * (1m/100cm)
Area = 0.8 # m^2
w = m.Var(lb=0) # width of the cardboard piece
x = m.Var(lb=0) # length of cut-out
h = m.Intermediate(Area / w) # Area = w h
box_width = m.Intermediate(w - 2 * x)
box_length = m.Intermediate(h - 2 * x)
box_height = m.Intermediate(x)
box_width_with_tabs = m.Intermediate(box_width + 2 * tabs)
Volume = m.Intermediate(box_width * box_length * box_height)
# upper constraint for box width with tabs
m.Equation(box_width_with_tabs < w)
# lower constraint for box width with tabs
m.Equations([box_width > 0,box_length > 0,Volume>0.01])
m.Obj(Volume) # how to maximize Volume?
m.solve()
print('width = ' + str(w.value[0]))
print('length = ' + str(h.value[0]))
print('height = ' + str(x.value[0]))
print('volume = ' + str(Volume.value[0]))
(:sourceend:)
Added lines 7-8:
A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).
Deleted lines 10-11:
A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).
Added lines 7-9:
* [[Attach:box_folding_problem.pdf | Box Folding Problem]]
* [[Attach:box_folding_solution.pdf | Box Folding Solution]]
* [[Attach:box_folding_solution.pdf | Box Folding Solution]]
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* [[Attach:box_folding_problem.pdf | Box Folding Problem]]
* [[Attach:box_folding_solution.pdf | Box Folding Solution]]
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[[Attach:box_folding_problem.pdf | Box Folding Problem]]
[[Attach:box_folding_solution.pdf | Box Folding Solution]]
[[Attach:box_folding_solution.pdf | Box Folding Solution]]
to:
* [[Attach:box_folding_problem.pdf | Box Folding Problem]]
* [[Attach:box_folding_solution.pdf | Box Folding Solution]]
* [[Attach:box_folding_solution.pdf | Box Folding Solution]]
Added lines 1-42:
(:title Box Folding Optimization:)
(:keywords box folding, project, nonlinear, optimization, engineering optimization, engineering design, interior point, active set, circle packing, packing optimization, python, matlab:)
(:description An optimization application to determine the maximum size of a box from a 0.8m^2 piece of cardboard.:)
!!!! Box Folding Optimization
A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).
Attach:box_folding.png
[[Attach:box_folding_problem.pdf | Box Folding Problem]]
[[Attach:box_folding_solution.pdf | Box Folding Solution]]
----
!!!! Download Sample Python Code
Python source code solves the box optimization problem with Newton's method, a quasi-Newton's method (BFGS), a steepest descent approach, and a conjugate gradient method. After the script executes, a figure appears that shows a contour plot of the solution with a graphical depiction of the progress of each method.
* [[Attach:Box_Folding_files.zip|Python Example Source Code]]
[[Attach:Box_Folding_files.zip|Attach:Box_Folding_files.png]]
Attach:box_folding_contour.png
----
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(:keywords box folding, project, nonlinear, optimization, engineering optimization, engineering design, interior point, active set, circle packing, packing optimization, python, matlab:)
(:description An optimization application to determine the maximum size of a box from a 0.8m^2 piece of cardboard.:)
!!!! Box Folding Optimization
A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).
Attach:box_folding.png
[[Attach:box_folding_problem.pdf | Box Folding Problem]]
[[Attach:box_folding_solution.pdf | Box Folding Solution]]
----
!!!! Download Sample Python Code
Python source code solves the box optimization problem with Newton's method, a quasi-Newton's method (BFGS), a steepest descent approach, and a conjugate gradient method. After the script executes, a figure appears that shows a contour plot of the solution with a graphical depiction of the progress of each method.
* [[Attach:Box_Folding_files.zip|Python Example Source Code]]
[[Attach:Box_Folding_files.zip|Attach:Box_Folding_files.png]]
Attach:box_folding_contour.png
----
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