MATLAB: Optimization for two output parameters varying three input variables within given constraints

optimization multiple output input variables constraints

Hi,

i am new to optimization in matlab. I have the optimization toolbox and would like to know how i could solve the following problem:

i have a created a function, lets call it simply f, that calculates the following two outputs over the cooling channels of a rocket engine nozzle:

the pressure drop (delta_p)
and temperature rise (delta_T)

This function f requires as variable input the following three parameters:

the number of cooling channels (n_chan)
the fixed width of a cooling channel (w_chan)
and a fixed aspect ratio (AR_chan) (which is the ratio of the height of a channel over the width, hence AR_chan=h_chan/w_chan).

so in short: function [delta_p,delta_T] = f(n_chan,w_chan,AR_chan)

Now i would like to find n_chan, w_chan and AR_chan such that delta_p is as low as possible while delta_T is as high as possible.

There are also the following six constraints to the optimization problem:

w_chan_min = 0.51e-3
h_chan_max = 5.1e-3
h_chan_min = w_chan_min
AR_chan_max = 8
AR_chan_min = h_chan_min/w_chan_min = 1
w_chan_max = h_chan_max/AR_chan_min = h_chan_max

is this possible and how would you suggest doing this?

thank you for looking at this problem! kind regards

Best Answer

You have two objectives: minimize delta_p while maximizing delta_T. In general, multiobjective optimization does not have a unique solution, only a set of Pareto optimal points. There is a bit of discussion in this section of the documentation. (Your problem might fit better into the discussion if you think about minimizing both delta_p and -delta_T.)

That said, you can sometimes formulate a problem so that fgoalattain gives you a reasonable solution. See this section of the documentation and this example.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

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MATLAB: Does the cellfun fails

"...however if I try to apply the same command again as..."

You have failed to take into account that inbetween running these two commands you have changed the data. So while the first cell array only contained scalar numeric (which is a bad way to store numeric data), the second time you call cellfun the cell array now also contains char vectors (lots of 'false', to be precise). Of course when you compare 'false'==1 then the output will be a vector like this:

>> 'false'==1
ans =
     0     0     0     0     0

and that is clearly not a scalar value, so your cellfun usage will fail unless you use 'uni',false and some more complex processing, or wrap the first argument function in any or something similar. Your third example give this error message

Function 'subsindex' is not defined for values of class 'cell'

because when you use the option 'UniformOutput',false then cellfun outputs a cell array, which cannot be used for indexing. So your attempt to use the output as an index will fail.

Here is a simpler approach using a numeric array (which it should be anyway):

>> m = cell2mat(a);
>> id0 = m==0;
>> id1 = m==1;
>> a(id0) = {'false'};
>> a(id1) = {'true'};
>> a
a = 
    'false'    'true'     [    2]    [    3]    [    4]    [    5]    [    6]    [    7]    [    8]    [    9]    [   10]    [   11]
    'true'     'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'
    [    2]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    3]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    4]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    5]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    6]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    7]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    8]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [    9]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [   10]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    [   11]    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'true'     'false'    'false'    'false'

Note that your row and column headers indicate that you should perhaps be using a table, or only storing the actual data (not the headers) in a simple numeric array. Then you could do this task very simply with some basic indexing:

>> c = {'false','true'};
>> b = c(1+m(2:end,2:end))
b = 
    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'false'    'false'    'false'    'false'
    'true'     'true'     'true'     'false'    'false'    'true'     'false'    'true'     'false'    'false'    'false'

MATLAB: How can i set the min and max size object to detect in matlab

The vision.CascadeObjectDetector object has properties MinSize and MaxSize. You can also pass 'MinSize' and 'MaxSize' name-value pairs into the object's constructor:

detector = vision.CascadeObjectDetector('MinSize', [32, 32]);

Best Answer

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MATLAB: Does the cellfun fails

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