I have a problem whose solution can be written as a binary string with a given length $N$, where $N$ is a given parameter. Standard GA works well on this problem. From runs of small values $N$, I found that optimal solutions are binary strings that contain only 01 or 011. For example, the optimal solution for $N=16$ is
0101011010101101. So I think it would be a good idea to only search the solutions space where all solutions/chromosomes only contain 01 or 011. But clearly the standard GA cannot restrict the search in the subspace I desire. One mutation or one crossover will make the new solution go into the larger solution space.
My question is: is there a way to adapt the standard GA to restrict its solution space to one where the chromosomes contain only 01 or 011?