Evolution Strategies

Evolution Strategies (ESs) were developed by Rechenberg and Schwefel at the Technical University of Berlin and have been extensively studied in Europe [Schw81] [Schw95] [Rech65] [Rech73].

While EP has derived for pure scientific interest, motivation of this study is, from the beginning, to solve engineering design problems: Rechenberg and Schwefel developed ESs in order to conduct successive wing tunnel experiments for aerodynamic shape optimization. Their important features are threefold:

  1. ESs use real-coding of design parameters since they model the organic evolution at the level of individual’s phenotypes.
  2. ESs depend on deterministic selection and mutation for its evolution.
  3. ESs use strategic parameters such as on-line self-adaptation of mutability parameters.

In evolutionary strategies, the representation used is a fixed-length real-valued vector. As with the bit-strings of genetic algorithms, each position in the vector corresponds to a feature of the individual. However, the features are considered to be behavioral rather than structural. “Consequently, arbitrary non-linear interactions between features during evaluation are expected which forces a more holistic approach to evolving solutions” [Ange96].

The main reproduction operator in evolutionary strategies is Gaussian mutation. Another operator that is used is intermediate recombination, in which the vectors of two parents are averaged together, element by element, to form a new offspring (see Figure 1).

Figure 5. Intermediate Recombination of Parents a) & b) to form Offspring c)

The effects of these operators reflect the behavioral as opposed to structural interpretation of the representation since knowledge of the values of vector elements is used to derive new vector elements.

The selection of parents to form offspring is less constrained than it is in genetic algorithms and genetic programming. For instance, due to the nature of the representation, it is easy to average vectors from many individuals to form a single offspring. In a typical evolutionary strategy, N parents are selected uniformly randomly (i.e., not based upon fitness), more than N offspring are generated through the use of recombination, and then N survivors are selected deterministically. The survivors are chosen either from the best N offspring (i.e., no parents survive) or from the best N parents and offspring [SJBF93].

Some examples of early applications of ESs are: optimal dimensioning of the core of a fast sodium-type breeder reactor [Heus70], shape optimization of vaulted reinforced concrete shells [Hart74], arm prosthesis design [Brud77], optimization of a thermal water jet propulsion system [Mark78].

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