Precise runtime analysis for plateaus

Denis Antipov, Benjamin Doerr

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

To gain a better theoretical understanding of how evolutionary algorithms cope with plateaus of constant fitness, we analyze how the (1 + 1) EA optimizes the n-dimensional Plateauk function. This function has a plateau of second-best fitness in a radius of k around the optimum. As optimization algorithm, we regard the (1 + 1) EA using an arbitrary unbiased mutation operator. Denoting by α the random number of bits flipped in an application of this operator and assuming (formula presented), we show the surprising result that for k ≥ 2 the expected optimization time of this algorithm is (formula presented) that is, the size of the plateau times the expected waiting time for an iteration flipping between 1 and k bits. Our result implies that the optimal mutation rate for this function is approximately k/en. Our main analysis tool is a combined analysis of the Markov chains on the search point space and on the Hamming level space, an approach that promises to be useful also for other plateau problems.

Original languageEnglish
Title of host publicationParallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings
EditorsCarlos M. Fonseca, Nuno Lourenco, Penousal Machado, Luis Paquete, Anne Auger, Darrell Whitley
PublisherSpringer Verlag
Pages117-128
Number of pages12
ISBN (Print)9783319992587
DOIs
Publication statusPublished - 1 Jan 2018
Event15th International Conference on Parallel Problem Solving from Nature, PPSN 2018 - Coimbra, Portugal
Duration: 8 Sept 201812 Sept 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11102 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Conference on Parallel Problem Solving from Nature, PPSN 2018
Country/TerritoryPortugal
CityCoimbra
Period8/09/1812/09/18

Keywords

  • Markov chains
  • Mutation
  • Runtime analysis
  • Theory

Fingerprint

Dive into the research topics of 'Precise runtime analysis for plateaus'. Together they form a unique fingerprint.

Cite this