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## Evolutionary Optimization with Cumulative Step Length Adaptation: A Performance Analysis

Citations: | 1 - 1 self |

### Citations

5155 | Optimization by simulated annealing
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ...plicitly by some simulation model. Among such strategies are certain stochastic approximation approaches [15, 19], implicit filtering [12], direct pattern search [21], variants of simulated annealing =-=[16]-=-, and a variety of evolutionary algorithms [5]. All of those strategies attempt to approach the optimum in a sequence of steps until some termination criterion is satisfied. For real-valued problems w... |

1188 |
Evolutionary Algorithms in Theory and Practice
- Bäck
- 1996
(Show Context)
Citation Context ...trategies are certain stochastic approximation approaches [15, 19], implicit filtering [12], direct pattern search [21], variants of simulated annealing [16], and a variety of evolutionary algorithms =-=[5]-=-. All of those strategies attempt to approach the optimum in a sequence of steps until some termination criterion is satisfied. For real-valued problems with objective functions of the form�� �, the a... |

546 | Completely derandomized self-adaptation in evolution strategies
- Hansen, Ostermeier
(Show Context)
Citation Context ...ds particular promise due to its ability to reliably adapt the entire mutation covariance matrix and that has been used successfully in industrial applications (see [17, 18] and further references in =-=[14]-=-) is the cumulative step length adaptation mechanism by Hansen and Ostermeier [13, 14]. That mechanism adapts step lengths by analyzing information from the sequence of most recently taken steps. Whil... |

541 | Handbook of Evolutionary Computation.
- Back, Fogel, et al.
- 1997
(Show Context)
Citation Context ...e for the problem at hand. A comprehensive overview of both theoretical results and of applications and case studies of evolution strategies and other types of evolutionary algorithms can be found in =-=[6]-=-. 2The present paper presents an analysis of the behavior of an evolution strategy with cumulative step length adaptation on a simple class of objective functions disturbed by noise. The algorithm an... |

365 | Parameter control in evolutionary algorithms.
- Eiben, Hinterding, et al.
- 1999
(Show Context)
Citation Context ...nction. The adaptation of step lengths can be based either on the outcome of trial steps or on the history of the search process. Parameter control methods for evolutionary algorithms are surveyed in =-=[11]-=-. One of the methods that holds particular promise due to its ability to reliably adapt the entire mutation covariance matrix and that has been used successfully in industrial applications (see [17, 1... |

239 |
The Theory of Evolution Strategies
- Beyer
- 2001
(Show Context)
Citation Context ...ria. Due to the difficulties involved, hardly any of the theoretical investigations of evolutionary algorithms in real-valued search spaces consider step length adaptation mechanisms. An exception is =-=[7]-=-, in which the behavior of a one-parent strategy with mutative self-adaptation is studied. A common approach to studying the properties of evolution strategies — a type of evolutionary algorithm often... |

87 | Adaptive stochastic approximation by the simultaneous perturbation method
- Spall
(Show Context)
Citation Context ...vative information is available. Such problems arise for example when the objective is given implicitly by some simulation model. Among such strategies are certain stochastic approximation approaches =-=[15, 19]-=-, implicit filtering [12], direct pattern search [21], variants of simulated annealing [16], and a variety of evolutionary algorithms [5]. All of those strategies attempt to approach the optimum in a ... |

76 | Toward a theory of evolution strategies: Self-adaptation - Beyer - 1996 |

63 | C.T.: An implicit filtering algorithm for optimization of functions with many local minima
- Gilmore, Kelley
- 1995
(Show Context)
Citation Context ...le. Such problems arise for example when the objective is given implicitly by some simulation model. Among such strategies are certain stochastic approximation approaches [15, 19], implicit filtering =-=[12]-=-, direct pattern search [21], variants of simulated annealing [16], and a variety of evolutionary algorithms [5]. All of those strategies attempt to approach the optimum in a sequence of steps until s... |

50 |
The Theory of Evolution Strategies. Natural Computing Series
- Beyer
- 2001
(Show Context)
Citation Context ... classes of objective functions that possess inherent symmetries that make the analysis mathematically tractable. An overview of that approach along with a number of important results can be found in =-=[8]-=-. Of course, there is no guarantee that results obtained under the assumption of such symmetries bear any relevance for practical optimization problems. However, recommendations with regard to the set... |

40 | On self-adaptive features in real-parameter evolutionary algorithms
- HG, Deb
- 2001
(Show Context)
Citation Context ...h much, even though significantly higher mutation strengths would achieve a better noise-to-signal ratio and greater progress. This insight sheds new light on the postulate suggested by Beyer and Deb =-=[10]-=- that in “flat” regions of the search space, i.e. in regions where the objective function values appear (nearly) constant, step length adaptation schemes should tend to systematically increase step le... |

39 | Noisy Optimization with Evolution Strategies.
- Arnold
- 2002
(Show Context)
Citation Context ...�-ES with cumulative step length adaptation is robust in that it degrades gradually with increasing noise levels. An empirical evaluation of direct optimization strategies in the presence of noise in =-=[3]-=- has shown that this is not necessarily true for other commonly used approaches, thus making the evolution strategy a promising candidate for the optimization of noisy objective functions. Acknowledgm... |

35 |
Verallgemeinerte individuelle Schrittweitenregelung in der Evolutionsstrategie. Mensch und Buch
- Hansen
- 1998
(Show Context)
Citation Context ...ariance matrix and that has been used successfully in industrial applications (see [17, 18] and further references in [14]) is the cumulative step length adaptation mechanism by Hansen and Ostermeier =-=[13, 14]-=-. That mechanism adapts step lengths by analyzing information from the sequence of most recently taken steps. While recommendations with respect to the setting of some of the strategy’s parameters hav... |

33 |
Stochastic Estimation of a Regression Function.
- Kiefer, Wolfowitz
- 1952
(Show Context)
Citation Context ...vative information is available. Such problems arise for example when the objective is given implicitly by some simulation model. Among such strategies are certain stochastic approximation approaches =-=[15, 19]-=-, implicit filtering [12], direct pattern search [21], variants of simulated annealing [16], and a variety of evolutionary algorithms [5]. All of those strategies attempt to approach the optimum in a ... |

25 | From Evolutionary Operation to Parallel Direct Search: Pattern Search Algorithms for Numerical Optimization,”
- Torczon, Trosset
- 1998
(Show Context)
Citation Context ...example when the objective is given implicitly by some simulation model. Among such strategies are certain stochastic approximation approaches [15, 19], implicit filtering [12], direct pattern search =-=[21]-=-, variants of simulated annealing [16], and a variety of evolutionary algorithms [5]. All of those strategies attempt to approach the optimum in a sequence of steps until some termination criterion is... |

17 | Qualms regarding the optimality of cumulative path length control in CSA/CMA-evolution strategies
- Beyer, Arnold
(Show Context)
Citation Context ... strategy’s parameters have been made in [14], questions concerning the optimal choice of population sizes and the practically relevant issue of robustness in the presence of noise that was raised in =-=[9]-=- have been left unaddressed. Theoretical investigations of parameter control strategies are important as they can not only yield an improved understanding of a strategy’s strengths and limitations, bu... |

14 | Performance analysis of evolution strategies with multi-recombination in high-dimensional R N -search spaces disturbed by noise. Theoretical Computer Science. Accepted for publication
- Arnold, Beyer
(Show Context)
Citation Context ...ge search space dimensionality, provided that the population size�is not too large. Improved estimates for the progress vector as well as the progress rate for moderate values of have been derived in =-=[1, 4]-=-. While the simple expressions quoted here form the basis for the calculations in Sect. 5, 6, and 7, those improved estimates will be used in Sect. 8 for numerically determining optimal population siz... |

11 | Optimisation of a stator blade used in a transonic compressor cascade with evolution strategies - Olhofer, Arima, et al. - 2000 |

9 |
H.G.: Local performance of the (=I ; )-ES in a noisy environment
- Arnold, Beyer
- 2000
(Show Context)
Citation Context ... signed length�of the central component of vector is defined (� to equal���if�points towards the target and to equal���if it points away from it. Introducing normalized quantities it has been seen in =-=[2]-=- that in the limit of high search space dimensionality ), the expected squared length of the progress vector and the expected signed length of its central component are 6�� �� � � Figure 2: Decomposi... |

9 |
Drag Reduction and Shape Optimization of Airship Bodies
- Lutz, Wagner
- 1997
(Show Context)
Citation Context ...n [11]. One of the methods that holds particular promise due to its ability to reliably adapt the entire mutation covariance matrix and that has been used successfully in industrial applications (see =-=[17, 18]-=- and further references in [14]) is the cumulative step length adaptation mechanism by Hansen and Ostermeier [13, 14]. That mechanism adapts step lengths by analyzing information from the sequence of ... |

9 | Theoretical comparisons of evolutionary computation and other optimization approaches - Spall, Hill, et al. - 1999 |

6 |
Optimisation of a stator blade used in a transonic compressor cascade with evolution strategies
- Olhofer, Arima, et al.
- 2000
(Show Context)
Citation Context ...n [11]. One of the methods that holds particular promise due to its ability to reliably adapt the entire mutation covariance matrix and that has been used successfully in industrial applications (see =-=[17, 18]-=- and further references in [14]) is the cumulative step length adaptation mechanism by Hansen and Ostermeier [13, 14]. That mechanism adapts step lengths by analyzing information from the sequence of ... |

4 |
Local Performance of Evolution Strategies in the Presence of Noise
- Arnold
- 2001
(Show Context)
Citation Context ...ge search space dimensionality, provided that the population size�is not too large. Improved estimates for the progress vector as well as the progress rate for moderate values of have been derived in =-=[1, 4]-=-. While the simple expressions quoted here form the basis for the calculations in Sect. 5, 6, and 7, those improved estimates will be used in Sect. 8 for numerically determining optimal population siz... |

1 | Evolutionary Algorithms in Theory and Practice - Brick - 1996 |