Is there a standard geometric way to apply cross over/mutation in a genetic algorithm

I am currently building a genetic algorithm to tune n parameters where n will probably be in the range of 3 n 8 but could be up to 15. I would like my initial population N (let's say N 1000) to be evenly dispersed across the input space. When calculating the next generation I surmised that the most effective way to combine parents would be to calculate the centroid, on the surface of the hypersphere, between some m nearest-neighbour parents. The larger m is, the fewer new points we would add. The rest being calculated in a similar fashion but from random parents.