# Completely Derandomized Self-Adaptation in Evolution Strategies

@article{Hansen2001CompletelyDS, title={Completely Derandomized Self-Adaptation in Evolution Strategies}, author={Nikolaus Hansen and Andreas Ostermeier}, journal={Evolutionary Computation}, year={2001}, volume={9}, pages={159-195} }

This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation. [...] Key Result If this objective is pursued rigor-ously, a completely derandomized self-adaptation scheme results, which adapts arbitrary normal mutation distributions. This scheme, called covariance matrix adaptation (CMA), meets the previously stated demands. It can still be considerably improved by cumulation - utilizing an evolution path rather than single searchâ€¦ Expand

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#### References

SHOWING 1-10 OF 67 REFERENCES

A Derandomized Approach to Self-Adaptation of Evolution Strategies

- Mathematics, Computer Science
- Evolutionary Computation
- 1994

This paper presents a derandomized scheme of mutative step-size control that facilitates a reliable self-adaptation of individual step-sizes and indicates that the adaptation by this concept declines due to an interaction of the random elements involved. Expand

Toward a Theory of Evolution Strategies: Self-Adaptation

- Computer Science, Mathematics
- Evolutionary Computation
- 1995

This paper analyzes the self-adaptation (SA) algorithm widely used to adapt strategy parameters of the evolution strategy (ES) in order to obtain maximal ES performance and shows that applying Schwefel's -scaling rule guarantees the linear convergence order of the ES. Expand

Directed mutation-a new self-adaptation for evolution strategies

- Computer Science
- Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406)
- 1999

The authors introduce a new type of self-adaptation that overcomes the disadvantages of the known types and experimental results based on the sphere model show a significant increase of performance. Expand

An Evolution Strategy with Coordinate System Invariant Adaptation of Arbitrary Normal Mutation Distr

- Mathematics
- 1999

A self-adaptation of arbitrary normal mutation distributions within the concept of mutative strategy parameter control (MSG) using a newly formulated mutation operator is introduced. The coordinateâ€¦ Expand

Invariance, Self-adaptation and Correlated Mutations in Evolution Strategies Invariance, Self-adaptation and Correlated Mutations in Evolution Strategies

- 2000

i are transformed accordingly to f tablet(1) or f tablet(1) , as shown in Table 2." must be \.. . where x (0) and (0) i are transformed accordingly to f tablet(1) or f tablet(5) , as shown in Tableâ€¦ Expand

On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation

- Computer Science
- ICGA
- 1995

A new adaptation scheme for adapting arbitrary normal mutation distributions in evolution strategies is introduced which can adapt correct scaling and correlations between object parameters and reliably adapts mutation distributions corresponding to hyperellipsoids with high axis ratio. Expand

Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation

- Mathematics, Computer Science
- Proceedings of IEEE International Conference on Evolutionary Computation
- 1996

A new formulation for coordinate system independent adaptation of arbitrary normal mutation distributions with zero mean is presented. This enables the evolution strategy (ES) to adapt the correctâ€¦ Expand

Mutate Large, But Inherit Small! On the Analysis of Rescaled Mutations in 1-lambda-ES with Noisy Fitness Data

- Computer Science
- PPSN
- 1998

It will be shown that standard self-adaptation has considerable problems to drive the ES in its optimum working regime, and remedies are provided to improve the self- Adaptation. Expand

A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization

- Mathematics, Medicine
- Evolutionary Computation
- 2002

The proposed generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (G3 model) are proposed and found to consistently and reliably perform better than all other methods used in the study. Expand

Mutate large, but inherit small ! On the analysis of rescaled mutations in (1, Î»)-ES with noisy fitness data

- Computer Science
- 1998

It will be shown that standard self-adaptation has considerable problems to drive the ES in its optimum working regime and remedies are provided to improve the self- Adaptation. Expand