I have a question about what to do with the fitnesses (fitness'?) that are 0 when getting the fitness proportionate probabilities. Should the container for the members be sorted by highest fitness first, then do code similar to this:
for all members of population
sum += fitness of this individual
end for
for all members of population
probability = sum of probabilities + (fitness / sum)
sum of probabilities += probability
end for
loop until new population is full
do this twice
number = Random between 0 and 1
for all members of population
if number > probability but less than next probability then you have been selected
end for
end
create offspring
end loop
My problem that I am seeing as I go through one iteration by hand with randomly generated members is that I have some member's fitness as 0, but when getting the probability of those members, it keeps the same probability as the last non zero member. Is there a way I can separate the non zero probabilities from the zero probabilities? I was thinking that even if I sort based on highest fitness, the last non zero member would have the same probability as the zero probabilities.
Consider this example:
individual fitness(i) probability(i) partial_sum(i)
1 10 10/20 = 0.50 0.50
2 3 3/20 = 0.15 0.5+0.15 = 0.65
3 2 2/20 = 0.10 0.5+0.15+0.1 = 0.75
4 0 0/20 = 0.00 0.5+0.15+0.1+0.0 = 0.75
5 5 5/20 = 0.25 0.5+0.15+0.1+0.0+0.25 = 1.00
------
Sum 20
Now if number = Random between [0;1[
we are going to pick individual i
if:
individual condition
1 0.00 <= number < partial_sum(1) = 0.50
2 0.50 = partial_sum(1) <= number < partial_sum(2) = 0.65
3 0.65 = partial_sum(2) <= number < partial_sum(3) = 0.75
4 0.75 = partial_sum(3) <= number < partial_sum(4) = 0.75
5 0.75 = partial_sum(4) <= number < partial_sum(5) = 1.00
If an individual has fitness 0
(e.g. I4) it cannot be selected because of its selection condition (e.g. I4 has the associated condition 0.75 <= number < 0.75
).