Minimize the Material to Build a Box
The purpose of this example is to minimize the amount of cardboard required
to build an open topped box with a volume of 500 cubic inches.
The image below shows the basic cardboard shape, where the dimensions “a” and “b”
define both the volume of the box and the surface area of the cardboard.
Feasible Pairs
The approach used will employ a feature called “Feasible Pairs”.
A feasible pair is defined by one input variable, one output variable.
There is also a specified, required value for the output variable.
At each call of the control routine, the value of the input variable is found
that results in the desired output value.
By using this approach, ONLY cases that are “feasible” (i.e. only boxes with 500 cubic inches)
will be examined.
In this case for example, at each evaluation, the value of “a” is found that results in
“Volume” being 500 in3.
This effectively changes the problem from being two dimensional in “a” and “b”,
to being a one dimensional minimize problem in “b” only.
The python file is very much like Examples 1 and 2, but now with a feasible pair addition.
We add a statement to define our feasible pair.
PS.makeFeasiblePair( outName="Volume", feasibleVal=500.0, inpName='a')
This “makeFeasiblePair” command simply says that our output variable is “Volume”,
its feasible value is 500.0, and that the input variable “a” is used to control
the value of Volume.
The defined range of “a” will be used as the search range to solve for Volume = 500 in3.
For the full text of the file, click the link below.
download fold_card_feas.py
The output from the minimize operation is shown below.
Best Box
| Design Variable Summary | | Design Variables (nominal values) | | Name | Value | Units | Description | | b | 10 | in | Height of Box (in) |
| Result Variables | | Name | Value | Units | Description | Low Limit | High Limit | | a | 7.07107
* -----> | in | Base Dimension of Cardboard (in)
(a varies to make Volume = 500 cuin) | >1 | <50 |
| Volume | 500 | cuin | Box Volume (cuin) | --- | --- |
| boxSurfArea | 332.843 | sqin | Box Surface Area (sqin) | --- | --- |
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PRIOR TO MINIMIZE OPTIMIZATION
| ParametricSoln: Feasible Optimization
====================== OPTIMIZATION DESIGN VARIABLES =======================
name value minimum maximum
b 10 2 10 Height of Box (in)
Figure of Merit: Box Surface Area (boxSurfArea) = 332.843 sqin <== Minimize
============================================================================
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AFTER MINIMIZE OPTIMIZATION
| ParametricSoln: Feasible Optimization
====================== OPTIMIZATION DESIGN VARIABLES =======================
name value minimum maximum
b 5 2 10 Height of Box (in)
Figure of Merit: Box Surface Area (boxSurfArea) = 300 sqin <== Minimize
============================================================================
|
| System Sensitivity |
 |
| Design Variables (nominal values) | | Name | Value | Units | Description | | b | 5 | in | Height of Box (in) |
| Result Variables | | Name | Value | Units | Description | Low Limit | High Limit | | a | 10
* -----> | in | Base Dimension of Cardboard (in)
(a varies to make Volume = 500 cuin) | >1 | <50 |
| Volume | 500 | cuin | Box Volume (cuin) | --- | --- |
| boxSurfArea | 300 | sqin | Box Surface Area (sqin) | --- | --- |
|
| Design Variable Summary | | Design Variables (nominal values) | | Name | Value | Units | Description | | b | 5 | in | Height of Box (in) |
| Result Variables | | Name | Value | Units | Description | Low Limit | High Limit | | a | 10
* -----> | in | Base Dimension of Cardboard (in)
(a varies to make Volume = 500 cuin) | >1 | <50 |
| Volume | 500 | cuin | Box Volume (cuin) | --- | --- |
| boxSurfArea | 300 | sqin | Box Surface Area (sqin) | --- | --- |
|
Parametric Solutions
parasol v0.1.7
contact: C. Taylor, cet@appliedpython.com
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