I'm trying to solve the shortest common supersequence with Genetic Algorithm. I found it a little bit hard to reduce the size of the chromosomes in each generation.
I know that the maximum size of the chromosome is the total length of the strings. Even if we create a "naive" genetic algorithm: Totally random strings (with different length) as initial population, mutation that replace a character, fitness that return how much strings that chromosome contains etc. How the crossover can reduce the size of the chromosome length? If we choose n-points crossover, the length of the children cannot be smaller than the shorter parent.
So how genetic algorithm can solve such problems that need the shortest chromosome length? How crossover can reduce the chromosome length?