Question

8.In the context of GAs(Genetic Algorithms) , when is a high mutation rate an advantage?

Answer 1

In GA, mutation operators are mostly used to provide exploration and cross-over operators are widely used to lead the population to converge on one the good solutions find so far (exploitation). Consequently, while cross-over tries to converge to a specific point in the landscape, the mutation does its best to avoid convergence and explore more areas.

Obviously, we prefer to explore much more at the beginning of the search process (to ensure the population coverage and diversity). On the other hand, we prefer more exploitations at the end of the search process to ensure the convergence of the population to the global optimum. There is just an exception; when population converges to a local optimum, we should (if we can) increase the population diversity to explore other areas.

According to the above facts, too high mutation rate increases the probability of searching more areas in search space, however, it prevents the population to converge to an optimum solution. On the other hand, too small mutation rates may result in premature convergence (falling to local optima instead of global optimum).In other words, too high mutation rate reduces the searchability of GA to a simple (and dummy!) random walk while a too-small GA (without any other facilities such as niching or crowd-avoiding to preserve diversity) almost always fails to a local optimum.

As Larry Raisanen mentioned, the best value of the mutation rate is very problem-specific. You can try several values in a linear or bidirectional manner. Remember, as Colin Reeves wrote, this value also depends on the nature and implementation of the algorithm. In my opinion, however, there is no constant best mutation rate for most of the real-world problems. As I mentioned before, the searching algorithm demands different exploration-exploitation abilities in different stages of the search process. Hence, a more dynamic mutation rate, as Paulo Gaspar proposed, is more preferred. I believe you can find more complex methods that adaptively tune the mutation rate according to the problem and the state of the current population comparing with the previous ones.