Hi Neda,

As is, this is not an optimization problem but a root-finding problem: https://en.wikipedia.org/wiki/Root-finding_algorithms

You have two ways to solve them: use root-finding methods (such as Newton-Raphson), or use actual optimization solvers like you suggested.

You can put these equations as constraints and define an arbitrary objective function (doesn't matter which one), or you can minimize the norm of the residuals (the differences between the right-hand sides and left-hand slides).

Since you want to use a genetic algorithm (although it most likely isn't the most appropriate method), I would say that you should minimize the norm of the residuals.

Dear Charlie Vanaret is the norm of residuals the same as what I did before? but now instead of finding zeros, I should minimize the equation, Am I right?

Hi Neda,

It would look something like this if you use the l2 norm:

min (T_inf + 8*a*S3/(3*pi*k) - Tc)^2 + ... (write here the rest)

Be aware that you can get stuck in a local minimum (a point that is the best in its neighborhood but still doesn't satisfy your equations).

Best,

Charlie

Hi Neda,

I can't understand problem? What does mean "the smallest overall error in the equations"?

Dear Maciej Karczyński It means the variables must satisfy the three above equations in the best way...

Dear Neda,

unfortunately problem is not clear still, at least for me. Again what does mean "satisfy the three equations in the best way..."?

How to express (calculate) it?

It seems, that without answer on that question cannot create objective function.

I give an example:

in data fitting, the best fit minimizes the sum of squared residuals (a residual being: the difference between an observed value, and the fitted value provided by a model).

Maybe ask your mentor for help?

Dear Maciej Karczyński this sentence is what the related article used for this problem, If you want, I can send you the source article, maybe that make it clear more

I kindly please attach this paper or send me one.