I am trying to solve the Zen Garden puzzle using an evolutionary algorithm. My question relates to evolutionary algorithms in general.

Bit about evolutionary algorithms: An evolutionary algorithm is an algorithm which tries to solve a given problem in a semi-random way. Most often I have seen it is implemented thusly: for a given starting state of the problem a generation of random solution approaches for is generated. Each speciemen (approach) has a set of genes which define it. Each speciemen is then used to try and find a solution to the problem. If no solutions are found, then we try to determine the fitness of each speciemen by some set of rules. For example- if the problem was to collect all treasures on a map, then the fitness a speciemen could be determined by the ammount of treasures it managed to collect. Once we determine their fitness we try to crossbreed the speciemen semi-randomly, giving higher chance of reproduction to those with higher fitness. This way we create a new generation of speciemen, where each of them has some genes from both of its parents. Then we try to solve the problem using the new generation of speciemen and the cycle goes on until a solution is found or we reach some kind of pre-determined limit of max-generations.

Question: Can the reproduction function which determines how speciemen (solution attempts) reproduce take into account some kind of gene strength to also determine which genes are best to be passed down to the child of two speciemen? What I mean by that is that for example if I could measure how much a certain gene contributed to the solution attempt can I give the gene a higher chance to be passed on or should child genes be passed on randomly?