crossover for integer encoding

Idea is to preserve relative order that elements occur
Informal procedure:
1. Choose an arbitrary part from the first parent
2. Copy this part to the first child
3. Copy the numbers that are not in the first part, to the first child:
starting right from cut point of the copied part,
using the order of the second parent
and wrapping around at the end
4. Analogous for the second child, with parent roles reversed
Copy randomly selected set from first parent
Copy rest from second parent in order 1,9,3,8,2
Informal procedure for parents P1 and P2:
Choose random segment and copy it from P1
Starting from the first crossover point look for elements in that segment of P2 that have not been copied
For each of these i look in the offspring to see what element j has been copied in its place from P1
Place i into the position occupied j in P2, since we know that we will not be putting j there (as is already in offspring)
If the place occupied by j in P2 has already been filled in the offspring k, put i in the position occupied by k in P2
Having dealt with the elements from the crossover segment, the rest of the offspring can be filled from P2.
Second child is created analogously
Basic idea:
Each allele comes from one parent together with its position.
Informal procedure:
1. Make a cycle of alleles from P1 in the following way.
(a) Start with the first allele of P1.
(b) Look at the allele at the same position in P2.
(c) Go to the position with the same allele in P1.
(d) Add this allele to the cycle.
(e) Repeat step b through d until you arrive at the first allele of P1.
2. Put the alleles of the cycle in the first child on the positions they have in the first parent.
3. Take next cycle from second parent