Non-elitist evolutionary algorithms excel in fitness landscapes with sparse deceptive regions and dense valleys

Duc-Cuong Dang, Anton Eremeev, Per Kristian Lehre

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Abstract

It is largely unknown how the runtime of evolutionary algorithms depends on fitness landscape characteristics for broad classes of problems. Runtime guarantees for complex and multi-modal problems where EAs are typically applied are rarely available.

We present a parameterised problem class SparseLocalOptα,ε where the class with parameters α, ϵ ∈ [0, 1] contains all fitness landscapes with deceptive regions of sparsity ε and fitness valleys of density α. We study how the runtime of EAs depends on these fitness landscape parameters.

We find that for any constant density and sparsity α, ε ∈ (0, 1), SparseLocalOptα,ε has exponential elitist (μ + λ) black-box complexity, implying that a wide range of elitist EAs fail even for mildly deceptive and multi-modal landscapes. In contrast, we derive a set of sufficient conditions for non-elitist EAs to optimise any problem in SparseLocalOptα,ε in expected polynomial time for broad values of α and ε. These conditions can be satisfied for tournament selection and linear ranking selection, but not for (μ, λ)-selection.
Original languageEnglish
Title of host publicationGECCO '21
Subtitle of host publicationProceedings of the Genetic and Evolutionary Computation Conference
EditorsFrancisco Chicano
Place of PublicationNew York
PublisherAssociation for Computing Machinery (ACM)
Pages1133–1141
Number of pages9
ISBN (Electronic)9781450383509
DOIs
Publication statusPublished - 26 Jun 2021
Event2021 Genetic and Evolutionary Computation Conference, GECCO 2021 - Virtual, Online, France
Duration: 10 Jul 202114 Jul 2021

Publication series

NameGenetic and Evolutionary Computation Conference (GECCO)
PublisherACM

Conference

Conference2021 Genetic and Evolutionary Computation Conference, GECCO 2021
Country/TerritoryFrance
CityVirtual, Online
Period10/07/2114/07/21

Bibliographical note

Funding Information:
Eremeev was supported by the Russian Science Foundation grant 17-18-01536. Lehre was supported by a Turing AI Fellowship (EPSRC grant ref EP/V025562/1).

Publisher Copyright:
© 2021 ACM.

Keywords

  • Elitism
  • Fitness landscape analysis
  • Runtime analysis

ASJC Scopus subject areas

  • Genetics
  • Computational Mathematics

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