How many and which parents should we select for crossover in genetic algorithm

Question

I have read many tutorials, papers and I understood the concept of Genetic Algorithm, but I have some problems to implement the problem in Matlab.

In summary, I have:

• A chromosome containing three genes [ a b c ] with each gene constrained by some different limits.

• Objective function to be evaluated to find the best solution

What I did:

• Generated random values of a, b and c, say 20 populations. i.e
  [a1 b1 c1] [a2 b2 c2]…..[a20 b20 c20]

• At each solution, I evaluated the objective function and ranked the solutions from best to worst.

Difficulties I faced:

• Now, why should we go for crossover and mutation? Is the best solution I found not enough?

• I know the concept of doing crossover (generating random number, probability…etc) but which parents and how many of them will be selected to do crossover or mutation?
  Should I do the crossover for the entire 20 solutions (parents) or only two of them?

Answer 1

Sharing a bit of advice from 'Practical Neural Network Recipies in C++' book... It is a good idea to have a significantly larger population for your first epoc, then your likely to include features which will contribute to an acceptable solution. Later epocs which can have smaller populations will then tune and combine or obsolete these favourable features.

And Handbook-Multiparent-Eiben seems to indicate four parents are better than two. However bed manufactures have not caught on to this yet and seem to only produce single and double-beds.

Answer 2

Generally a Genetic Algorithm is used to find a good solution to a problem with a huge search space, where finding an absolute solution is either very difficult or impossible. Obviously, I don't know the range of your values but since you have only three genes it's likely that a good solution will be found by a Genetic Algorithm (or a simpler search strategy at that) without any additional operators. Selection and Crossover is usually carried out on all chromosome in the population (although it's not uncommon to carry some of the best from each generation forward as is). The general idea is that the fitter chromosomes are more likely to be selected and undergo crossover with each other.

Mutation is usually used to stop the Genetic Algorithm prematurely converging on a non-optimal solution. You should analyse the results without mutation to see if it's needed. Mutation is usually run on the entire population, at every generation, but with a very small probability. Giving every gene 0.05% chance that it will mutate isn't uncommon. You usually want to give a small chance of mutation, without it completely overriding the results of selection and crossover.

As has been suggested I'd do a lit bit more general background reading on Genetic Algorithms to give a better understanding of its concepts.