---
_id: '1112'
abstract:
- lang: eng
  text: There has been renewed interest in modelling the behaviour of evolutionary
    algorithms by more traditional mathematical objects, such as ordinary differential
    equations or Markov chains. The advantage is that the analysis becomes greatly
    facilitated due to the existence of well established methods. However, this typically
    comes at the cost of disregarding information about the process. Here, we introduce
    the use of stochastic differential equations (SDEs) for the study of EAs. SDEs
    can produce simple analytical results for the dynamics of stochastic processes,
    unlike Markov chains which can produce rigorous but unwieldy expressions about
    the dynamics. On the other hand, unlike ordinary differential equations (ODEs),
    they do not discard information about the stochasticity of the process. We show
    that these are especially suitable for the analysis of fixed budget scenarios
    and present analogs of the additive and multiplicative drift theorems for SDEs.
    We exemplify the use of these methods for two model algorithms ((1+1) EA and RLS)
    on two canonical problems(OneMax and LeadingOnes).
author:
- first_name: Tiago
  full_name: Paixao, Tiago
  id: 2C5658E6-F248-11E8-B48F-1D18A9856A87
  last_name: Paixao
  orcid: 0000-0003-2361-3953
- first_name: Jorge
  full_name: Pérez Heredia, Jorge
  last_name: Pérez Heredia
citation:
  ama: 'Paixao T, Pérez Heredia J. An application of stochastic differential equations
    to evolutionary algorithms. In: <i>Proceedings of the 14th ACM/SIGEVO Conference
    on Foundations of Genetic Algorithms</i>. ACM; 2017:3-11. doi:<a href="https://doi.org/10.1145/3040718.3040729">10.1145/3040718.3040729</a>'
  apa: 'Paixao, T., &#38; Pérez Heredia, J. (2017). An application of stochastic differential
    equations to evolutionary algorithms. In <i>Proceedings of the 14th ACM/SIGEVO
    Conference on Foundations of Genetic Algorithms</i> (pp. 3–11). Copenhagen, Denmark:
    ACM. <a href="https://doi.org/10.1145/3040718.3040729">https://doi.org/10.1145/3040718.3040729</a>'
  chicago: Paixao, Tiago, and Jorge Pérez Heredia. “An Application of Stochastic Differential
    Equations to Evolutionary Algorithms.” In <i>Proceedings of the 14th ACM/SIGEVO
    Conference on Foundations of Genetic Algorithms</i>, 3–11. ACM, 2017. <a href="https://doi.org/10.1145/3040718.3040729">https://doi.org/10.1145/3040718.3040729</a>.
  ieee: T. Paixao and J. Pérez Heredia, “An application of stochastic differential
    equations to evolutionary algorithms,” in <i>Proceedings of the 14th ACM/SIGEVO
    Conference on Foundations of Genetic Algorithms</i>, Copenhagen, Denmark, 2017,
    pp. 3–11.
  ista: 'Paixao T, Pérez Heredia J. 2017. An application of stochastic differential
    equations to evolutionary algorithms. Proceedings of the 14th ACM/SIGEVO Conference
    on Foundations of Genetic Algorithms. FOGA: Foundations of Genetic Algorithms,
    3–11.'
  mla: Paixao, Tiago, and Jorge Pérez Heredia. “An Application of Stochastic Differential
    Equations to Evolutionary Algorithms.” <i>Proceedings of the 14th ACM/SIGEVO Conference
    on Foundations of Genetic Algorithms</i>, ACM, 2017, pp. 3–11, doi:<a href="https://doi.org/10.1145/3040718.3040729">10.1145/3040718.3040729</a>.
  short: T. Paixao, J. Pérez Heredia, in:, Proceedings of the 14th ACM/SIGEVO Conference
    on Foundations of Genetic Algorithms, ACM, 2017, pp. 3–11.
conference:
  end_date: 2017-01-15
  location: Copenhagen, Denmark
  name: 'FOGA: Foundations of Genetic Algorithms'
  start_date: 2017-01-12
date_created: 2018-12-11T11:50:12Z
date_published: 2017-01-12T00:00:00Z
date_updated: 2021-01-12T06:48:22Z
day: '12'
department:
- _id: NiBa
doi: 10.1145/3040718.3040729
language:
- iso: eng
month: '01'
oa_version: None
page: 3 - 11
publication: Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic
  Algorithms
publication_identifier:
  isbn:
  - 978-145034651-1
publication_status: published
publisher: ACM
publist_id: '6255'
quality_controlled: '1'
scopus_import: 1
status: public
title: An application of stochastic differential equations to evolutionary algorithms
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...