On Easiest Functions for Mutation Operators in Bio-Inspired OptimisationReport as inadecuate

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, Volume 78, Issue 2, pp 714–740

First Online: 18 August 2016Received: 30 September 2015Accepted: 09 August 2016DOI: 10.1007-s00453-016-0201-4

Cite this article as: Corus, D., He, J., Jansen, T. et al. Algorithmica 2017 78: 714. doi:10.1007-s00453-016-0201-4


Understanding which function classes are easy and which are hard for a given algorithm is a fundamental question for the analysis and design of bio-inspired search heuristics. A natural starting point is to consider the easiest and hardest functions for an algorithm. For the 1+1 EA using standard bit mutation SBM it is well known that OneMax is an easiest function with unique optimum while Trap is a hardest. In this paper we extend the analysis of easiest function classes to the contiguous somatic hypermutation CHM operator used in artificial immune systems. We define a function MinBlocks and prove that it is an easiest function for the 1+1 EA using CHM, presenting both a runtime and a fixed budget analysis. Since MinBlocks is, up to a factor of 2, a hardest function for standard bit mutations, we consider the effects of combining both operators into a hybrid algorithm. We rigorously prove that by combining the advantages of k operators, several hybrid algorithmic schemes have optimal asymptotic performance on the easiest functions for each individual operator. In particular, the hybrid algorithms using CHM and SBM have optimal asymptotic performance on both OneMax and MinBlocks. We then investigate easiest functions for hybrid schemes and show that an easiest function for a hybrid algorithm is not just a trivial weighted combination of the respective easiest functions for each operator.

KeywordsRunning time analysis Theory Hybridisation Evolutionary algorithms Artificial immune systems 

Author: Dogan Corus - Jun He - Thomas Jansen - Pietro S. Oliveto - Dirk Sudholt - Christine Zarges

Source: https://link.springer.com/

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