Population Size vs. Mutation Strength for the (1+λ) EA on OneMax
Christian Gießen, Carsten Witt · 2015
The (1+1) EA with mutation probability c/n, where c>0 is an arbitrary constant, is studied for the classical OneMax function. Its expected optimization time is analyzed exactly (up to lower order terms) as a function of c and λ. It turns out that 1/n is the only optimal mutation probability if λ=o(ln n ln ln n/ln ln ln n), which is the cut-off point for linear mnspeed-up. However, if λ is above this cut-off point then the standard mutation probability 1/n is no longer the only optimal choice. Instead, the expected number of generations is (up to lower order terms) independent of c, irrespectively of it being less than 1 or greater.