Problem $4$: Genetic Algorithm

Given a population of $4$ initial position in a $4x4$ board of $N-$queens given as the column

vector $($:$1,3,2,4$:$),($:$1,1,1,1$:$),($:$1,2,3,4$:$),($:$1,1,2,4$:$),$ calculate which board

position is good based upon number of mutually attacking queens, then use the crossover

by cross segments $1$:$2$ and $3$:$4$ of two best positions together and two worst positions

together, and including them in the pool if it they are better than one of the previous

positions. If any new one is not then one of the column values of the newly created

vector is properly mutated to reduce the number of attacking queens, and the suitability to

include in the pool is checked again. Population is fixed to the value $4.$ The worst

solutions after the cycle are removed from consideration. Repeat this process for two

cycles of cross overs, mutation and give the final pool.