Optimal Mutation Rate Control under Selection in Hamming Spaces

We investigate the effect of selection in a meta-genetic algo- rithm designed to optimize mutation rate control, based on the fitness of sequences relative to a defined optimum, in asexual evolution. Multiple innovations in the algorithm are required to achieve the evolution of optimal mutation rate control un- der selection. Before implementing selection, results from this improved algorithm clarify the optimal relationship of mutation rate to distance from the optimum as being a dou- ble sigmoid for binary sequences. Furthermore, the results clarify how such control functions depend on alphabet size, sequence length and the time horizon over which evolution is assessed. Incorporating selection leads to a distinctive shape of optimal mutation rate control function. This function has a mutation rate less that a third of 1/length at a Hamming dis- tance of one from the optimum and beyond. This surprising result for a simple, universally monotonic single-peaked fit- ness landscape highlights the need for further research using models such as this. Future work will therefore explore how this control function may vary, for instance with population size and alternative selection mechanisms common in Artifi- cial Life models.