All One Problem (with 1000 binary genes, assuming 1 is good gene while 0 is not. 
- Starting with '1' and '0' both being 50%
=> We can see the number of good genes '1' increase as evelution goes. But we need to be lucky to obtain all '1' chromosomes when number of population is small, say, 100.
- With 1 being only 0.1%
Then what will happen if the number of good gene '1' is extremely few, say, 0.1% instead of 50%? Assuming one chromosome has 1000 genes, average number of good gene '1' at the begining is only 1 while number of gene '0' being 999.
(i) Population number: 100 vs. 7000 ... By Potapchuk Sergey
=> Quite amazingly, the number of '1' increases but when the initial population is small such as 100 it saturates immatualy. One way to avoid this immatured saturation (called "Local Optimum"), we might increase the number of population. See, the number of '1' in the best chromosome in each population vs. generation.
(ii) Population number: 100, 1000, 3000, 5000, 6500 and 9000 ... Doronin Nikolai
=> We can see that all the genes in the best chromosom are '1' if we start with an enough amount of initial population.
(i) Mutate genes an average of one out of thousand (mutation rate is 0.001) in a similar evolution of 1000 gene chromosomes with '1' and '0' both being 50% ... Meshco Evgenii
=> When we have mutation we can see that much smaller population is enough to obtain the solution than evolution without mutation. In this example, number of population 100 lead to success while 20 was too small to reach all-one chromosome.
(ii) Or, experiment to know how population size influences the result ... By Bogush Anatoluy
=> When we have mutation we can see that much smaller population is enough to obtain the solution than evolution without mutation. See even 50 chromosomes evolved to all one chromosomes.
Multi-dimensional function minimization