On the impact of objective function transformations on evolutionary and black-box algorithms

Different fitness functions describe different problems. Hence, certain fitness transformations can lead to easier problems although they are still a model of the considered problem. In this paper, the class of neutral transformations for a simple rank-based evolutionary algorithm (EA) is described completely, i.e., the class of functions that transfers easy problems for this EA in easy ones and difficult problems in difficult ones. Moreover, the class of neutral transformations for this population-based EA is equal to the black-box neutral transformations. Hence, it is a proper superset of the corresponding class for an EA based on fitness-proportional selection, but it is a proper subset of the class for random search. Furthermore, the minimal and maximal classes of neutral transformations are investigated in detail.