Runtime analysis of the (1 + (λ, λ)) genetic algorithm on random satisfiable 3-CNF formulas

Maxim Buzdalov, Benjamin Doerr

Research output: Chapter in Book/Report/Conference proceedingConference Proceeding (Non-Journal item)

Abstract

The (1 + (λ, λ)) genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on some optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA profited from the perfect fitness-distance correlation. In this work, we conduct a rigorous runtime analysis of this GA on random 3-SAT instances in the planted solution model having at least logarithmic average degree, which are known to have a weaker fitness distance correlation.

We prove that this GA with fixed not too large population size again obtains runtimes better than Θ(n log n), which is a lower bound for most evolutionary algorithms on pseudo-Boolean problems with unique optimum. However, the self-adjusting version of the GA risks reaching population sizes at which the intermediate selection of the GA, due to the weaker fitness-distance correlation, is not able to distinguish a profitable offspring from others. We show that this problem can be overcome by equipping the self-adjusting GA with an upper limit for the population size. Apart from sparse instances, this limit can be chosen in a way that the asymptotic performance does not worsen compared to the idealistic OneMax case. Overall, this work shows that the (1 + (λ, λ)) GA can provably have a good performance on combinatorial search and optimization problems also in the presence of a weaker fitness-distance correlation.
Original languageEnglish
Title of host publicationGECCO '17
Subtitle of host publicationProceedings of the Genetic and Evolutionary Computation Conference
PublisherAssociation for Computing Machinery
Pages1343-1350
Number of pages8
ISBN (Print)978-1-4503-4920-8
DOIs
Publication statusPublished - 01 Jul 2017
Externally publishedYes
EventGECCO 2017: The Genetic and Evolutionary Computation Conference -
Duration: 15 Jul 201719 Jul 2017

Conference

ConferenceGECCO 2017
Period15 Jul 201719 Jul 2017

Keywords

  • azuma inequality
  • fitness=distance correlation
  • genetic algorithm
  • random instances
  • runtime analysis
  • satisfiability
  • theory

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