Log-linear convergence and divergence of the scale-invariant \((1+1)\)-ES in noisy environments

DOI10.1007/s00453-010-9403-3zbMath1230.68212OpenAlexW2075208118MaRDI QIDQ633840

Anne Auger, Mohamed Jebalia, Nikolaus Hansen

Publication date: 30 March 2011

Published in: Algorithmica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00453-010-9403-3

zbMATH Keywords

convergenceconvergence ratesMarkov chainsBorel-Cantelli lemmaevolution strategiesnumerical optimizationnoisy optimizationstochastic optimization algorithms

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Stochastic programming (90C15) Approximation methods and heuristics in mathematical programming (90C59) Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Randomized algorithms (68W20)

Related Items (6)

Algorithm portfolios for noisy optimization ⋮ Principled Design of Continuous Stochastic Search: From Theory to Practice ⋮ Linear Convergence of Comparison-based Step-size Adaptive Randomized Search via Stability of Markov Chains ⋮ Analysing the robustness of evolutionary algorithms to noise: refined runtime bounds and an example where noise is beneficial ⋮ Analysis of runtime of optimization algorithms for noisy functions over discrete codomains ⋮ Average convergence rate of evolutionary algorithms in continuous optimization

Uses Software

• CEC 05

Cites Work

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• Markov chains and stochastic stability
• Global convergence for evolution strategies in spherical problems: Some simple proofs and difficulties.
• Convergence results for the (1,\(\lambda\))-SA-ES using the theory of \(\varphi\)-irreducible Markov chains
• A comparison of evolution strategies with other direct search methods in the presence of noise
• Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
• Probability with Martingales
• Foundations of Genetic Algorithms
• Foundations of Genetic Algorithms

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