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I want to use PSO to optimize a 3D problem using real data (lat, long, alt). How is this accomplished? I see in the examples and tutorials it is done against existing surface plots; Rosenbrock, Ackley, Griewank, etc.. How do I run it against real numbers?

R2020b

Walter Roberson
on 19 Sep 2020

You use whatever formula is appropriate. For example

d=load('In_Flight_Data.mat') ;

lat=d.lat;

long=d.long;

alt=d.alt;

fun = @(x) sum((x(1)-lat).^2 + (x(2)-long).^2 + (x(3)-tan(alt)).^2);

pso(fun, 3)

John D'Errico
on 19 Sep 2020

You can't. That is, the optimal is just the optimal value at each point in your sample. You cannot do better than that, at least, not unless you are willing to build a model of the process.

So, what are you willing to do in terms of a model? What do you know? What are you willing to assume? If you cannot build a model, then you cannot do any form of optimization that will have some chance of being better than the best point from your data.

If your data is at all noisy, then don't expect to do well of course. But one option might be to use an interpolating spline surface model. Again, noise will totally destroy any spline fit, making it useless for this purpose.

Walter Roberson
on 22 Sep 2020

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