## A Survey of Evolution Strategies (1991)

Venue: | Proceedings of the Fourth International Conference on Genetic Algorithms |

Citations: | 226 - 3 self |

### BibTeX

@INPROCEEDINGS{Bäck91asurvey,

author = {Thomas Bäck and Frank Hoffmeister and Hans-Paul Schwefel},

title = {A Survey of Evolution Strategies},

booktitle = {Proceedings of the Fourth International Conference on Genetic Algorithms},

year = {1991},

pages = {2--9},

publisher = {Morgan Kaufmann}

}

### Years of Citing Articles

### OpenURL

### Abstract

Similar to Genetic Algorithms, Evolution Strategies (ESs) are algorithms which imitate the principles of natural evolution as a method to solve parameter optimization problems. The development of Evolution Strategies from the first mutation--selection scheme to the refined (¯,)--ES including the general concept of self--adaptation of the strategy parameters for the mutation variances as well as their covariances are described. 1 Introduction The idea to use principles of organic evolution processes as rules for optimum seeking procedures emerged independently on both sides of the Atlantic ocean more than two decades ago. Both approaches rely upon imitating the collective learning paradigm of natural populations, based upon Darwin's observations and the modern synthetic theory of evolution. In the USA Holland introduced Genetic Algorithms in the 60ies, embedded into the general framework of adaptation [Hol75]. He also mentioned the applicability to parameter optimization which was fir...

### Citations

2827 |
Adaptation in natural and artificial systems
- Holland
- 1975
(Show Context)
Citation Context ...ations, based upon Darwin's observations and the modern synthetic theory of evolution. In the USA Holland introduced Genetic Algorithms in the 60ies, embedded into the general framework of adaptation =-=[Hol75]-=-. He also mentioned the applicability to parameter optimization which was first realized in the work of De Jong [Jon75]. This article focuses on the German development called Evolution Strategies (ESs... |

662 |
Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog
- Rechenberg
- 1973
(Show Context)
Citation Context ...tion which was first realized in the work of De Jong [Jon75]. This article focuses on the German development called Evolution Strategies (ESs), introduced by Rechenberg at Berlin in the 60ies as well =-=[Rec73]-=-, and further developed by Schwefel [Sch75b]. ESs were applied first to experimental optimization problems with more or less continuously changeable parameters only. The first numerical applications w... |

511 |
Numerical Optimization of Computer Models
- Schwefel
- 1981
(Show Context)
Citation Context ...c d \Delta oe t ; if p t s ! 1=5 c i \Delta oe t ; if p t s ? 1=5 oe t ; if p t s = 1=5 (12) where p t s is the frequency of successful mutations, measured e.g. over intervals of 10n trials. Schwefel =-=[Sch81]-=- gives reasons to use the factors c d = 0:82 and c i = 1=0:82 for the adjustment, which should take place every n mutations. It should be noted that with (6) and (12) the operator m consists of a rand... |

375 |
Simulated Annealing and Boltzmann Machines
- Aarts
- 1989
(Show Context)
Citation Context ...Then, for the limit value f ~ f = lim t!1 f(x t ) under the assumption ~ f ? f a contradiction emerges, such that ~ f = f must be valid. As is well known from similar theorems for Simulated Annealing =-=[AK89]-=- and Genetic Algorithms [EAH91], such results are not of much practical relevance due to the unlimited time condition. In fact, we are interested in the expectation of the convergence rate ', which is... |

190 | Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie. Interdisciplinary systems research; 26. Birkhäuser - Schwefel - 1977 |

187 |
An Analysis of the Behaviour of a Class of Genetic Adaptive Systems", Doctoral Thesis - University of Michigan, Dissertational Abstracts International
- DeJong
- 1975
(Show Context)
Citation Context ...netic Algorithms in the 60ies, embedded into the general framework of adaptation [Hol75]. He also mentioned the applicability to parameter optimization which was first realized in the work of De Jong =-=[Jon75]-=-. This article focuses on the German development called Evolution Strategies (ESs), introduced by Rechenberg at Berlin in the 60ies as well [Rec73], and further developed by Schwefel [Sch75b]. ESs wer... |

93 | A variant of evolution strategies for vector optimization
- Kursawe
- 1991
(Show Context)
Citation Context ..., HB91]. Current research concerning ESs deals with applications like the travelling salesman problem [Her91, Rud91], girder--bridge optimization [Loh91], neural networks [Sal91], vector optimization =-=[Kur91]-=-, and parameter optimization in general [BBK84, Bor78, BB79]. Furthermore the scalable parallelism of such an Evolutionary Algorithm [Hof91] is investigated with the help of implementations on MIMD--c... |

78 |
Evolutionsstrategie und numerische optimierung
- Schwefel
(Show Context)
Citation Context ...f De Jong [Jon75]. This article focuses on the German development called Evolution Strategies (ESs), introduced by Rechenberg at Berlin in the 60ies as well [Rec73], and further developed by Schwefel =-=[Sch75b]-=-. ESs were applied first to experimental optimization problems with more or less continuously changeable parameters only. The first numerical applications were performed by Hartmann [Har74] and Hofler... |

62 |
Kybernetische Evolution als Strategie der experimentellen Forschung in der Strömungsmechanik
- Schwefel
- 1965
(Show Context)
Citation Context ...lems like the optimization of a PID regulator within a highly nonlinear system. Besides of simulating different versions of the strategy on the first available digital computer at the TUB, a Zuse Z23 =-=[Sch65]-=-, computers soon were also used to solve numerical optimization problems by means of the first versions of simple ESs [Har74, Hof76]. The algorithm used in these applications was a simple mutation--se... |

48 | Genetic algorithms and evolution strategies: similarities and differences - Hoffmeister, Back - 1991 |

40 |
Collective phenomena in evolutionary systems
- Schwefel
- 1987
(Show Context)
Citation Context ... limited life span allows to forget inappropriate internal parameter settings. This may result in short phases of recession, but it avoids long stagnation phases due to misadapted strategy parameters =-=[Sch87]-=-. The (+)--ES and (,)--ES fit into the same formal framework with the only difference being the limited life time of individuals in (,)--ES. Thus, only a formal description of a (,)--ES is presented h... |

40 | R.: Parallel Problem Solving from Nature - Schwefel, Männer - 1991 |

18 |
Evolutionsstrategien zur numerischen Losung von Adaptationsaufgaben
- Born
- 1978
(Show Context)
Citation Context ... considerations all components of oe t are identical, i.e. 8 i; j 2 f1; : : : ; ng : oe t i = oe t j =: oe. For a (1+1)--ES and a regular optimization problem a convergence property can be shown (see =-=[Bor78]-=-). The regularity of the optimization problem is specified by the criteria given in definition 1. Definition 1 The optimization problem (1) is called regular , iff the following conditions are satisfi... |

16 | Global optimization by means of distributed evolution strategies - Rudolph - 1991 |

14 |
Global convergence of genetic algorithms: An infinite Markov chain analysis
- Eiben, Aarts, et al.
- 1991
(Show Context)
Citation Context ...f = lim t!1 f(x t ) under the assumption ~ f ? f a contradiction emerges, such that ~ f = f must be valid. As is well known from similar theorems for Simulated Annealing [AK89] and Genetic Algorithms =-=[EAH91]-=-, such results are not of much practical relevance due to the unlimited time condition. In fact, we are interested in the expectation of the convergence rate ', which is given by the quotient of the d... |

12 | Scalable Parallelism by Evolutionary Algorithms, pages 177–198. Number 367 - Hoffmeister - 1991 |

10 |
Application of Evolution Strategy in Parallel Populations
- Lohmann
- 1990
(Show Context)
Citation Context ...ng difference between ESs and Genetic Algorithms [HB90, HB91]. Current research concerning ESs deals with applications like the travelling salesman problem [Her91, Rud91], girder--bridge optimization =-=[Loh91]-=-, neural networks [Sal91], vector optimization [Kur91], and parameter optimization in general [BBK84, Bor78, BB79]. Furthermore the scalable parallelism of such an Evolutionary Algorithm [Hof91] is in... |

7 | Application of the evolutionsstrategie to discrete optimization problems, in: H.-P. Schwefel, R. Männer (Eds.), Parallel Problem Solving from - Herdy - 1991 |

4 |
Binare optimierung durch somatische Mutation
- Schwefel
- 1975
(Show Context)
Citation Context ...re performed by Hartmann [Har74] and Hofler [Hof76], and a first attempt towards extending this strategy in order to solve discrete or even binary parameter optimization problems was made by Schwefel =-=[Sch75a]-=-. baeck@lumpi.informatik.uni-dortmund.de y iwan@lumpi.informatik.uni-dortmund.de z uin005@ddohrz11.bitnet The aim of this paper is to give an overview of the development of ESs, beginning with the fir... |

3 |
Improved convergence rate of back-propagation with dynamic adaptation of the learning rate
- Salomon
- 1991
(Show Context)
Citation Context ... and Genetic Algorithms [HB90, HB91]. Current research concerning ESs deals with applications like the travelling salesman problem [Her91, Rud91], girder--bridge optimization [Loh91], neural networks =-=[Sal91]-=-, vector optimization [Kur91], and parameter optimization in general [BBK84, Bor78, BB79]. Furthermore the scalable parallelism of such an Evolutionary Algorithm [Hof91] is investigated with the help ... |

2 | Parallelisierungsmoglichkeiten fur direkte Optimierungsverfahren auf Transputersystemen - Bormann - 1989 |

2 |
Optimierung balkenartiger Zylinderschalen aus Stahlbeton mit elastischem und plastischem Werkstoverhalten [Optimization of beamlike cylindrical shells in reinforced concrete including elastic and plastic material behaviour
- Hartmann
- 1974
(Show Context)
Citation Context ... Schwefel [Sch75b]. ESs were applied first to experimental optimization problems with more or less continuously changeable parameters only. The first numerical applications were performed by Hartmann =-=[Har74]-=- and Hofler [Hof76], and a first attempt towards extending this strategy in order to solve discrete or even binary parameter optimization problems was made by Schwefel [Sch75a]. baeck@lumpi.informatik... |

1 | Numerische Parameteroptimierung in mathematischen Modellen mittels einer Evolutionsstrategie - Born, Bellmann - 1979 |

1 | Evolution strategies in numerical optimization on vector computers - Bernutat-Buchmann, Krieger - 1984 |

1 |
Formoptimierung von Leichtbaufachwerken durch Einsatz einer Evolutionsstrategie
- Hofler
- 1976
(Show Context)
Citation Context ... ESs were applied first to experimental optimization problems with more or less continuously changeable parameters only. The first numerical applications were performed by Hartmann [Har74] and Hofler =-=[Hof76]-=-, and a first attempt towards extending this strategy in order to solve discrete or even binary parameter optimization problems was made by Schwefel [Sch75a]. baeck@lumpi.informatik.uni-dortmund.de y ... |