The theory of evolution strategies
The theory of evolution strategies
Theoretical Computer Science
Convergence results for the (1, λ)-SA-ES using the theory of ϕ-irreducible Markov chains
Theoretical Computer Science
Completely Derandomized Self-Adaptation in Evolution Strategies
Evolutionary Computation
Reconsidering the progress rate theory for evolution strategies in finite dimensions
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Toward a theory of evolution strategies: On the benefits of sex---the (μ/μ, λ) theory
Evolutionary Computation
Lower Bounds for Evolution Strategies Using VC-Dimension
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Covariance Matrix Adaptation Revisited --- The CMSA Evolution Strategy ---
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
On the Parallel Speed-Up of Estimation of Multivariate Normal Algorithm and Evolution Strategies
EvoWorkshops '09 Proceedings of the EvoWorkshops 2009 on Applications of Evolutionary Computing: EvoCOMNET, EvoENVIRONMENT, EvoFIN, EvoGAMES, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, EvoNUM, EvoSTOC, EvoTRANSLOG
Log-linear convergence and optimal bounds for the (1 + 1)-ES
EA'07 Proceedings of the Evolution artificielle, 8th international conference on Artificial evolution
Log-Linear Convergence and Divergence of the Scale-Invariant (1+1)-ES in Noisy Environments
Algorithmica - Special Issue: Theory of Evolutionary Computation
Optimal weighted recombination
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
| Hi-index | 0.00 |
Evolution Strategies (ESs) are population-based methods well suited for parallelization. In this paper, we study the convergence of the (µ/µw, λ)-ES, an ES with weighted recombination, and derive its optimal convergence rate and optimal µ especially for large population sizes. First, we theoretically prove the log-linear convergence of the algorithm using a scale-invariant adaptation rule for the step-size and minimizing spherical objective functions and identify its convergence rate as the expectation of an underlying random variable. Then, using Monte-Carlo computations of the convergence rate in the case of equal weights, we derive optimal values for µ that we compare with previously proposed rules. Our numerical computations show also a dependency of the optimal convergence rate in ln(λ) in agreement with previous theoretical results.