How can I do calibration of empirical equations via genetic algorithm by using optimization GUI toolbox in MATLAB to find best fit values of the constant coefficient of empirical equations? If you don't mind please explain step by step procedure
in optimisation GUI toolbox of MATLAB.
The GA tool in Matlab is powerful, but requires some trial and error before to provide good results.
The first thing to do is to prepare an "objective function": a function that:
1. takes as input the set of parameters to be calibrated,
2. "run the model": in your case, it must compute the empirical equations and compare them to some measurements
3. calculate the goodness of fit, via one criterion like Nash for time-series or RMSE.
4. gives as output the value of the criterion. Remark: GA tool minimizes, so if your criterion "C" has to be maximized, the function must return "-C"
With this you can already try to run the GA with basic settings.
An important point: in hydrology, normally your parameters are independent one from the other, so you don't have to put linear constraints and so on. However, they have physical ranges. I suggest you to spend some time in well defining the ranges of variation of your parameters, if you don't wont to come up at the end with absurd results like negative soil conductivity.
The GA allows you to define ranges, but in this case it forces you to use specific "mutation functions". Try it.
However, in my experience, GA options for unconstrained problems are much more effective (but maybe this changed with new versions?). If GA doesn't give satisfactory results, and you want to try unconstrained options, you can modify your objective function with some transformation. I used:
% x is the parameter
% vmin is the bottom of the range
% vmax is the top of the range
delta=vmax-vmin
x=atan(x)/pi+1/2; % this bring your x from unconstrained to (0,1)
x=x*delta+vmin; % this bring your x in (vmin, vmax)
Sir, I have 1000 data sets for training.. 5 inputs and one output.... I have another set of output data by using empirical equation... My objective is to reduce the differene between actual output and output obtained by using empirical equation.... Sir, what should be the objective function ..? How to write objective function in matlab script..? And how to find modified constant values for empirical equation.. I mean equation that best suited for my local conditions... I would like to do un constrained method
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