Optimisation of three function in two variables
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Alessandro Matteuzzi
il 1 Ott 2024
Commentato: Steven Lord
il 1 Ott 2024
Hi, i have three sperimantal eqation that describe: Temperature (T), Pressure (P) and refraction (R). Each function dependes from two variables x and y. So T=f(x,y), Pf(x,y) and R=f(x,y). I kwon the range of valure for x and y, so x1<x<x2 and y1<y<y2.
I want to maximise each of the functions, so i want to find the best couple of value for x and y that optimise the functions.
What is the best strategy?
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Star Strider
il 1 Ott 2024
To begin with, you need to parameterise the functions so that ‘x’ and ‘y’ are two elements in the same vector.
Your functions then become:
% b(1) = x, b(2) = y
T = f(b(1),b(2)) ...;
P = f(b(1),b(2)) ...;
R = f(b(1),b(2)) ...;
and the bounds become:
lb = [x1, y1];
ub = [x2, y2];
You can then use these with the fmincon functiion, for example. Optimise in ‘b’ and if you want to get the maxima, negate them in tthe fmincon call.
.
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John D'Errico
il 1 Ott 2024
There may be an issue here, if you think you can maximize them all simultaneously. The (x,y) coordinates that maximizes one function need not be (and almost certainly will not be) the same as that which maximizes the other responses.
Of course, if you are willing to find a different extremal point for each objective, then you just call a tool like fmincon three times, once for each objective.
Is there any recourse? I assume what you want to do is called multi-criteria optimization, or multi-objective optimization.
Here the common idea is to optimize a weighted sum of all three objectives. If, for example, the three objectives have completely different units or scaling, surely you want to weight them to counter that, possibly making them each roughly of the same importance in the result.
The tool in MATLAB to solve this general problem is fgoalattain.
help fgoalattain
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Steven Lord
il 1 Ott 2024
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