How to do crossover and mutation in one GA iteration process?

Question

I am learning genetic algorithms. I am trying to demonstrate one GA interation process for the problem as follows: X, Y and Z are the three integer variables ranges between 0 to 3, and there are initial population (Po) given as

x y z
1 0 3
1 2 0

Now I am trying to find the binary representation of the variables and apply crossover and mutation.

x=1 y=0 z=3              001 000 011
x=1 y=2 z=0              001 010 000

Next generation

Crossover

001 000 011
001 010 000

After crossover 

010 000 011
001 001 000

I am not sure if I did the two point crossover correctly. Please correct me if am wrong and help me get the result after mutation. So, that I can apply the fitness function to get the best solution found in the next generation.

Answer 1

I didn't quite follow how you applied the cross over, but there are probably many variations of this. Here is one method of binary GA's where Crossover and Mutation on binary variables work similarly as with regular variables.

First join the 3 genes into a single chromosome. Then choose two cross over points in the chromosome.

Parent 1 : 001 000 011 => 001000011
Parent 2 : 001 010 000 => 001010000

Lets suppose we choose the first crossover point between bits 2-3 and the second point between 7-8.

Parent 1 : 00 100001 1
Parent 2 : 00 101000 0

Then we create the first child by selecting the first and third sections from parent one, then the second section from parent two. Vice Versa for the second child.

Child 1 : 00 101000 1 => 001010001
Child 2 : 00 100001 0 => 001000010

Mutation is also similar but it happens at the bit level. Lets say child 2's 5th bit was selected for mutation. Then it becomes

Child 2 : 001010010

After this, the children are broken down back into genes and the fitness function can be computed

Child 1 : 001010001 => 001 010 001 => 1 2 1
Child 2 : 001010010 => 001 010 010 => 1 2 2

Here is a nice article describing the entire binary GA algorithm