Eight Queens with Evolutionary Computing

Example: Some valid solutions are given as follows:
V = 〈8, 3, 1, 6, 2, 5, 7, 4〉
V = 〈4, 2, 5, 8, 6, 1, 3, 7〉
It should also be noted that in this scheme number of solution candidates is
reduced to permutations P of 8:
where
and
4.2 Fitness function
#{P} = 8! = 40320
S ⊂ P ⊂ C
#{S} = 92
In Section 4.1 we deduced a formula to represent each distinct solution as a
vector:
V = 〈c1, c2, . . . , c8〉
Each vector can be thought of a complete genotype (genome) to solve the
Eight Queens Problem. Hence a genome in this sense is equivalent to a solution.
Each element of the vector can be thought as a gene expressing a queen being
present at a given square. The overall genetic combination shall determine the
final fitness score such that no two queens can check each other.
Let number of checks in a given vector be:
0