Genetic Programming and Evolvable Machines

, Volume 7, Issue 2, pp 171–193 | Cite as

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

  • Tobias Storch


Different objective functions characterize different problems. However, certain fitness transformations can lead to easier problems although they are still a model of the considered problem. In this article, the class of not worsening transformations for a simple population-based evolutionary algorithm (EA) is described completely. That is the class of functions that transfers easy problems in easy ones and difficult problems in difficult ones. Surprisingly, this class \(\mathcal{T}_{{\rm rank}}\) for the rank-based EA equals that for all black-box algorithms. The importance of the black-box algorithms' knowledge of the transformation is also pointed out. Hence, a comparison with the class \(\mathcal{T}_{{\rm prop}}\) of not worsening transformations for a similar EA which applies fitness-proportional selection, shows that \(\mathcal{T}_{{\rm rank}}\) is a proper superset of \(\mathcal{T}_{{\rm prop}}\). Moreover, \(\mathcal{T}_{{\rm rank}}\) is a proper subset of the corresponding class for random search. Finally, the minimal and maximal classes of not worsening transformations are described completely, too.


Evolutionary algorithm Black-box algorithm Runtime analysis 



This research was supported by the GIF, the German-Israeli Foundation for Scientific Research and Development, and the DFG, the German Research Foundation.The author thanks Stefan Droste, Ingo Wegener, and the referees for their help while improving this paper.


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer Science IIUniversity of DortmundDortmundGermany

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