Why Genetic Programming result is not consistent?

Hello

Dear experts

I am working on finding a relationship on some input parameters (X1, ... , X5) and an output parameter (Y). I am using Genetic Programming Toolbox in MATLAB and the provided example and just changed the input/output data to build my own equation. The problem is that every time I run the program it finds different parameters as "the best" model with different values for fitness and mse!

I don't know if that's how GP works, but is there any way that I make the code be in a way that considers all possible functions ('+','*',...) and find the best model?

I will attach my program here.

Thank you in advance for your help :)

[Stephen23]

"I am using Genetic Programming Toolbox in MATLAB and the provided example ..."

You linked to a FEX page, which contains third-party code. Of course neither TMW (the makers of MATLAB) nor any volunteer on this forum can explain how some random person's code should work, without spending a lot of time reverse engineering it: if you want to know how their code works, you should ask its author.

"is there any way that I make the code be in a way that considers all possible functions ('+','*',...) and find the best model?"

It sounds like you might want Global Search:

https://www.mathworks.com/help/gads/globalsearch.html

[Stephen23]

Benjamin's "Answer" moved here:

Dear Stephen, thank you for your response.

Well, I added Genetic Programming Toolbox from MATLAB add-ons, that's why I didn't assume just a random person exchanged that.

Regarding the GA optimizer, I just didn't know if that is something appropriate to my problem.

My goal is to develop an simple equation using some input parameters (X's) to predict Y, having any possible functions such as '+','-','/','exp','ln', and I came acroos with GP and I found that helpful!

Thank you for letting me know about Global Search and GA optimizer tools. I will try to see how I can use them.

[Stephen23]

@Benjamin: sorry, my mistake for confusing Genetic Programming with Genetic Algorithm ... a momentary synaptic lapse (hangs head in shame).

While FEX is a great resource of third-party code, you have to be very selective about choosing which submissions are worthwhile using or not: that might be a well-written toolbox... or it might not be. In any case, contact its author if there is something that you want to know that is not answered by reading its documentation.

[Benjamin]

Oh no need to apologize Stephen :) I appreciate you response.

It is just interesting to me that such helpful Toolbox that MATLAB provides doesn't have a comprehensive documentation, and even not many ask and answers on Matlab community!

Answer 1

[Walter Roberson]

Genetic programming is always random.

And NO there is no way to get it to consider all combinations of operations while still using genetic programming: it is part of the definition of genetic programming.

[Benjamin]

Thank you Walter for you answer.

Do you have any suggestion on what is the best method to achieve my goal (finding a relationship between some X's parameters and Y in which there is no individual X-Y relationship) ?

Can I still use GP, and play with the functions and/or run multiple times to find an acceptable equation?

(P.S. Sorry if my question looks naive, lol)

Regards,

[Walter Roberson]

If you were to discover through the searches that,

X1 - X3/log(X4)
---------------
X2 * (X4^(X3 - log(X1)*X2)) - X3^(X2 - exp(X1))
                              -----------------
                              X4 / (log(X3) - X2)
                              

gives a marginally better fit for Y... then chances are that you should be throwing that all out and starting over again.

Remember, that if you iterate through a bunch of models, then one of them is going to come out with the lowest residue. That doesn't mean that the one with the lowest residue one has any relationship at all to the true physics of the situation; there are a lot of mathematical accidents.

[Walter Roberson]

I just spent a while fitting using the model

a1*X1^a2 + a3*X2^a4 + a5*X3^a6 + a7*X4^a8 + a8*X5^a9

At the moment the best residue I have found for that is near

+5.89527e-12 * X1^(14.0668) - 2.43172e+06 * X2^(-6.07609) - 141.217 * X3^(4.97211) + 1.36918e+07 * X4^(-16.9352) + 0.00796812 * X5^(0.000446426)

but that is a barely different residue from (for example)

+5.59686e-11 * X1^(15.8437) - 333705 * X2^(-5.46948) - 64.2897 * X3^(5.41647) + 1.36918e+07 * X4^(-11.4162) + 0.00838126 * X5^(0.115229) 

Mathematical accidents. Cobbling together a formula that generates a marginally better residue is useless when you have no reason to believe that the formula has relevance to the real world.