How to choose population and generations for GA?

Hello everyone,

I would like to know if there is a method to properly define a good number of generations and population for running an optimization with GA? Is there any rule of thumb to choose the correct order of magnitude of those two parameters?

Thank you in advance

Answer 1

[Star Strider]

I use an optimoptions structure for this.

Example —

PopSz = 500;
Parms = 3;
opts = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms).*[1E-3 1E-1 1E+2], 'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf, 'PlotInterval',1);

It is then possible to scale the individual columns of the 'InitialPopulationMatrix' aas I do here, so that it is easier for ga to find an appropriate solution. Providing a relatively large number of rows (individuals) can slightly slow the function, however in my experience it decreases the number of generations required for ga to converge.

[vittorio sartoretto]

ok, thank you for your answer, but I don't get how it is possible to choose a good number of generations and population. In my optimization problem I have three design varibales: the first can assume 809 different values, the second can assume 1100 different values and the third can assume any value between 37 and 143; moreover I'm trying to optimize eight cost functions. I am quite sure that the default values for generation and population are not enough but how can I find out which would be a correct values for both?

[Star Strider]

In my optimoptions call, I set:

'MaxGenerations',2E3

because in my ismulations the default is not enough for ga to converge. The ga function generally does not require 2000 generations, however it usually requires more than the default. I doubt that there is any specific number of generations that will work in every problem.

For your 'InitialPopulationMatrix', you might want to do something like this:

N = 500;                                                % Number Of Individuals
IPM = [randi(250, N, 2) randi([37 143], N, 1)];         % Initial Population MAtrix

This sets the first 2 columns to go from (1,250) and the third column restricted to be between 37 and 143. Note that ga also allows bounds on the parameters, so you can restrict them as necessary. The initial values in the matrix need to be between those bounds (using an approach such I use here for the third column), if at all possible. Set the bounds in the ga call itself, not in the optimoptions structure.

I have no idea what problem you are solving or what your fitness function looks like, however allowing a large number of generations is likely necessary.

Also consider the approach in How to save data from Genetic Algorithm in case MATLAB crashes? since this appears to be a problem that will require a relatively long time to converge.

[vittorio sartoretto]

Thank you very much for your answer. I have a final question, is it usefull to specify the initial population matrix even if I have no idea where the minima of the problem are? Would a random initial population matrix allow the algorithm to find the solution sooner?

[Star Strider]

My pleasure!

‘... is it usefull to specify the initial population matrix even if I have no idea where the minima of the problem are?’

In my opinion, yes.

‘Would a random initial population matrix allow the algorithm to find the solution sooner?’

In my opinion, yes, especially if you have some idea of what the optimal parameter values are, you can either specify them and their ranges (this is easiest with randi) or scale them (as I did in my initial post here) to make it easier for ga to optimise them. Also, setting bounds on the parameters, if you know what their ranges should be, is more likely to produce a correct solution.

[vittorio sartoretto]

ok, I got it. Thank you for your answers

[Star Strider]

My pleasure!