question...

[Matthew Wall]

i'm afraid i do not have any research references for you on this one, 
but i can offer some anecdotal advice.

determining a popluation size depends on many factors:

1)  how much genetic material is in each genome (so how much of the
     search space is represented in a given population)?
2)  how well does the crossover operator 'move' the genetic algorithm
     through the search space (how likely is it to create individuals that
     are different than its parents)?
3)  how well does the crossover operator 'focus' the genetic algorithm
     through the search space (how likely is it to create individuals that
     are similar to its parents)?
4)  how long are you willing to wait to find a solution?
5)  how much computing power do you have at your disposal?  how long does
     it take to evaluate each individual?  how much ram does each individual
     use up?
6)  how violently does the mutation operator affect the genetic structure
     vs how much does it affect the genome score?  (this is a specific case
     of 'what is the correlation between genetic structure and objective
     measure?')

if (2) works properly, then having a small population size relative 
to the number of genes won't be too bad - the algorithm will simply 
have to run longer.

these are confounded somewhat by the linkages between the objective 
function and fitness scaling, also by the mapping of objective 
function to genotype vs objective function to phenotype.  (if you 
have a many-to-one mapping, i.e. two distinctly different genomes can 
have identical scores, then you will probably need a larger 
population and might want to use some kind of niching methods in your 
genetic algorithm)

years ago i did runs using 3D binary representations with over 10000 
genes in them and population sizes of 50 to 100.  everything worked 
just fine, but the took a long time to do it.  increasing the 
population size helped (more likeliehood of better individuals sooner 
in the evolution), but i ran into computing resource limits (not 
enough ram or cpu cycles to handle it).

hope this helps.  and, as always, i'm curious to know how things work out.

matthew


>Hi,
>
>Is there any rule of thumb stating someting on the relation between
>population size and chromosome length?
>
>To state it differently, what to do when the cromosome is build up of over
>120000 genes? has someone any experience in this?
>
>many thanks,
>
>Peter


Matthew Wall
mwall at domesolutions.CAN_THE_SPAM.com