Genetic Algorithm as Search

How GA search can be viewed as sampling the hyperspace

Schema   maps to planes in hypercube...
plane 0 * * ...
2 planes   0 * * ...   and * * 1 ...   becomes edge  0 * 1 ....

Crossover

one-point crossover, left and right bit don't have the same prob. of disruption.  The left bit has prob.  1/(L-1)   where L is the length of schema.   The right bit has  prob. 1.0
        1 ** ... ** 1

under two-point crossover   this schema has two bits that are "close together" hence has less disruption.  two-point cross can be visualize as "ring".   From this point of view  one-point is more disruptive.  (one-point becomes having one location fixed at the joint of the ring).

The ability of GA to search effectively comes from its "Implicit parallelism", i.e. one schema searches many hyperplanes.  GA focuses the search effort to the area of high prob. to find solution.   It spends more sampling near the plane where the highly fit individual located.  GA searches without "gradient" information.

Implementation

Selection

j = 0
partsum = 0
r = rand * sumfitness    // sumfitnes is the sum of population fitness
repeat
  j = j+1
  partsum = partsum + pop[j].fit
until (partsum > r ) or ( j = popsize )
return j