Mudasir - from your previous posts, I think that you have written your own version of the genetic algorithm and are not using that from the Global Optimization Toolbox. So depending upon how you have written the code to initialize the chromosomes, do the selection, do the crossover, do the mutation, then that all that will impact what happens when you increase the number of chromosomes (size of population). What do you observe about your initial population when you increase the size from 5 to 20? Do the genes in each chromosome vary significantly? How does the crossover affect the new chromosomes? When does convergence occur (i.e. at which generation)? I think that you will need to analyze the chromosomes to see how they change from one generation to the next. That analysis may explain why increasing the population size seems to have no affect on producing different/better results.
As for the elite strategy, the above link goes on to say that a fixed number of "elite children" are chosen for the next generation. These elite members have the best (i.e. lowest) fitness of the current generation and are "copied" in to the next generation as is. The remaining members of the next generation's population is made up of the children created through crossover and/or mutation. So this processing would occur prior to selection and crossover. See the example (from the link) for more details.
