Crossover can simulate bounded tree search on a fixed-parameter tractable optimization problem

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6 Scopus citations

Abstract

We investigate the effect of crossover in the context of parameterized complexity on a well-known fixed-parameter tractable combinatorial optimization problem known as the closest string problem. We prove that a multi-start (+1) GA solves arbitrary length-n instances of closest string in 2O(d 2+d log k) · poly(n) steps in expectation. Here, k is the number of strings in the input set, and d is the value of the optimal solution. This confirms that the multi-start (+1) GA runs in randomized fixed-parameter tractable (FPT) time with respect to the above parameterization. On the other hand, if the crossover operation is disabled, we show there exist instances that require nΩ(log(d+k)) steps in expectation. The lower bound asserts that crossover is a necessary component in the FPT running time.

Original languageEnglish (US)
Title of host publicationGECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference
PublisherAssociation for Computing Machinery, Inc
Pages1531-1538
Number of pages8
ISBN (Electronic)9781450356183
DOIs
StatePublished - Jul 2 2018
Event2018 Genetic and Evolutionary Computation Conference, GECCO 2018 - Kyoto, Japan
Duration: Jul 15 2018Jul 19 2018

Publication series

NameGECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference

Other

Other2018 Genetic and Evolutionary Computation Conference, GECCO 2018
CountryJapan
CityKyoto
Period7/15/187/19/18

Keywords

  • Crossover
  • Evolutionary algorithms
  • Fixed-parameter tractability
  • Parameterized complexity
  • Recombination
  • Theory

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