On Easiest Functions for Mutation Operators in Bio-Inspired Optimisation

Dogan Corus, Jun He, Thomas Jansen, Pietro S. Oliveto, Dirk Sudholt, Christine Zarges

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

139 Wedi eu Llwytho i Lawr (Pure)


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 an hybrid algorithm is not just a trivial weighted combination of the respective easiest functions for each operator.
Iaith wreiddiolSaesneg
Tudalennau (o-i)714–740
Rhif cyhoeddi2
Dyddiad ar-lein cynnar18 Awst 2016
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 01 Meh 2017

Ôl bys

Gweld gwybodaeth am bynciau ymchwil 'On Easiest Functions for Mutation Operators in Bio-Inspired Optimisation'. Gyda’i gilydd, maen nhw’n ffurfio ôl bys unigryw.

Dyfynnu hyn