optimization for two output parameters varying three input variables within given 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:

1. the pressure drop (delta_p)
2. and temperature rise (delta_T)

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

1. the number of cooling channels (n_chan)
2. the fixed width of a cooling channel (w_chan)
3. 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:

1. w_chan_min = 0.51e-3
2. h_chan_max = 5.1e-3
3. h_chan_min = w_chan_min
4. AR_chan_max = 8
5. AR_chan_min = h_chan_min/w_chan_min = 1
6. 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

[Matt J]

I assume w_chan_min/max are bounds on w_chan, but what are h_chan_max/min bounds on? You haven't mentioned an unknown variable h_chan.

[Ruwan]

yes w_chan_min and w_chan_max are the bounds on w_chan. h_chan is not an input but a direct result from the input, namely from the cooling channel aspect ratio AR_chan and the cooling channel width w_chan follows h_chan (h_chan = AR_chan*w_chan, where AR_chan actually is the aspect ratio of h_chan over w_chan)). Though both AR_chan and w_chan each have bounds, the resulting channel height h_chan also has bounds. Hence though a combination of w_chan and AR_chan might be within their bounds, the h_chan could be outside this bounds if not constrained.

Answer 1

[Alan Weiss]

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

[Ruwan]

i feared as much that it might not be as simple as i hoped it would be. Thanks for the links, i'll go through the documentation and hope i can figure it out! :)