Editing Evolutionary algorithm (section)

=== Virtual alphabets ===
With the theory of virtual alphabets, [[David E. Goldberg]] showed in 1990 that by using a representation with real numbers, an EA that uses classical [[Crossover (genetic algorithm)|recombination operators]] (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers.<ref>{{Citation |last=Goldberg |first=David E. |title=The theory of virtual alphabets |date=1990 |url=http://link.springer.com/10.1007/BFb0029726 |work=Parallel Problem Solving from Nature |series=Lecture Notes in Computer Science |volume=496 |pages=13–22 |publication-date=1991 |editor-last=Schwefel |editor-first=Hans-Paul |place=Berlin/Heidelberg |publisher=Springer-Verlag |language=en |doi=10.1007/bfb0029726 |isbn=978-3-540-54148-6 |access-date=2022-10-22 |editor2-last=Männer |editor2-first=Reinhard|url-access=subscription }}</ref> This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion.<ref>{{Cite book |last1=Stender |first1=J. |url=https://www.worldcat.org/oclc/47216370 |title=Genetic algorithms in optimisation, simulation, and modelling |last2=Hillebrand |first2=E. |last3=Kingdon |first3=J. |date=1994 |publisher=IOS Press |isbn=90-5199-180-0 |location=Amsterdam |oclc=47216370}}</ref><ref>{{Cite book |last=Michalewicz |first=Zbigniew |url=https://www.worldcat.org/oclc/851375253 |title=Genetic Algorithms + Data Structures = Evolution Programs |date=1996 |publisher=Springer |isbn=978-3-662-03315-9 |edition=3rd |publication-place=Berlin Heidelberg |oclc=851375253}}</ref>