Improved runtime bounds for the (1+1) EA on random 3-CNF formulas based on fitness-distance correlation

Benjamin Doerr, Frank Neumann, Andrew M. Sutton

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

With this paper, we contribute to the theoretical understanding of randomized search heuristics by investigating their behavior on random 3-SAT instances. We improve the results for the (1+1) EA obtained by Sutton and Neumann. [PPSN 2014, 942-951] in three ways. First, we reduce the upper bound by a linear factor and prove that the (1+1) EA obtains optimal solutions in time O (nlog n) with high probability on asymptotically almost all high-density satisfiable 3-CNF formulas. Second, we extend the range of densities for which this bound holds to satisfiable formulas of at least logarithmic density. Finally, we complement these mathematical results with numerical experiments that summarize the behavior of the (1+1) EA on formulas along the density spectrum, and suggest that the implicit constants hidden in our bounds are low. Our proofs are based on analyzing the run of the algorithm by establishing a fitness-distance correlation. This approach might be of independent interest and we are optimistic that it is useful for the analysis of randomized search heuristics in various other settings. To our knowledge, this is the first time that fitness-distance correlation is explicitly used to rigorously prove a performance statement for an evolutionary algorithm.

Original languageEnglish (US)
Title of host publicationGECCO 2015 - Proceedings of the 2015 Genetic and Evolutionary Computation Conference
EditorsSara Silva
PublisherAssociation for Computing Machinery, Inc
Pages1415-1422
Number of pages8
ISBN (Electronic)9781450334723
DOIs
StatePublished - Jul 11 2015
Event16th Genetic and Evolutionary Computation Conference, GECCO 2015 - Madrid, Spain
Duration: Jul 11 2015Jul 15 2015

Publication series

NameGECCO 2015 - Proceedings of the 2015 Genetic and Evolutionary Computation Conference

Other

Other16th Genetic and Evolutionary Computation Conference, GECCO 2015
CountrySpain
CityMadrid
Period7/11/157/15/15

Keywords

  • Fitness-distance correlation
  • Runtime analysis
  • Satisfiability

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