An application of stochastic differential equations to evolutionary algorithms

T. Paixao, J. Pérez Heredia, in:, Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, ACM, 2017, pp. 3–11.

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Conference Paper | Published | English
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Abstract
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).
Publishing Year
Date Published
2017-01-12
Proceedings Title
Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms
Page
3 - 11
Conference
FOGA: Foundations of Genetic Algorithms
Conference Location
Copenhagen, Denmark
Conference Date
2017-01-12 – 2017-01-15
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Paixao T, Pérez Heredia J. An application of stochastic differential equations to evolutionary algorithms. In: Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. ACM; 2017:3-11. doi:10.1145/3040718.3040729
Paixao, T., & Pérez Heredia, J. (2017). An application of stochastic differential equations to evolutionary algorithms. In Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms (pp. 3–11). Copenhagen, Denmark: ACM. https://doi.org/10.1145/3040718.3040729
Paixao, Tiago, and Jorge Pérez Heredia. “An Application of Stochastic Differential Equations to Evolutionary Algorithms.” In Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, 3–11. ACM, 2017. https://doi.org/10.1145/3040718.3040729.
T. Paixao and J. Pérez Heredia, “An application of stochastic differential equations to evolutionary algorithms,” in Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, Copenhagen, Denmark, 2017, pp. 3–11.
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.
Paixao, Tiago, and Jorge Pérez Heredia. “An Application of Stochastic Differential Equations to Evolutionary Algorithms.” Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, ACM, 2017, pp. 3–11, doi:10.1145/3040718.3040729.

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