Theoretical analysis of rank-based mutation - combining exploration and exploitation

Parameter setting is an important issue in the design of evolutionary algorithms. Experimental work has pointed out that it is often not useful to work with a fixed mutation rate. Therefore it was proposed that the population be ranked according to fitness and the mutation rate of an individual should depend on its rank. The claim is that this allows the algorithm to explore new regions in the search space as well as progress quickly towards optimal solutions. Complementing the experimental investigations, we examine the proposed approach by presenting rigorous theoretical analyses which point out the differences of rank-based mutation compared to a standard approach using a fixed mutation rate. To this end we theoretically explain the behaviour of rank-based mutation on various fitness landscapes proposed in the experimental work and present new significant classes of functions where the use of rank-based mutation may be both beneficial or detrimental compared to fixed mutation strategies.