Editing Genetic algorithm (section)

=== Chromosome representation ===
{{main | genetic representation }}
The simplest algorithm represents each chromosome as a [[Bit array|bit string]]. Typically, numeric parameters can be represented by [[integer]]s, though it is possible to use [[floating point]] representations. The floating point representation is natural to [[Evolution strategy|evolution strategies]] and [[evolutionary programming]]. The notion of real-valued genetic algorithms has been offered but is really a misnomer because it does not really represent the building block theory that was proposed by [[John Henry Holland]] in the 1970s. This theory is not without support though, based on theoretical and experimental results (see below). The basic algorithm performs crossover and mutation at the bit level. Other variants treat the chromosome as a list of numbers which are indexes into an instruction table, nodes in a [[linked list]], [[associative array|hashes]], [[object (computer science)|objects]], or any other imaginable [[data structure]]. Crossover and mutation are performed so as to respect data element boundaries. For most data types, specific variation operators can be designed. Different chromosomal data types seem to work better or worse for different specific problem domains.

When bit-string representations of integers are used, [[Gray coding]] is often employed. In this way, small changes in the integer can be readily affected through mutations or crossovers. This has been found to help prevent premature convergence at so-called ''Hamming walls'', in which too many simultaneous mutations (or crossover events) must occur in order to change the chromosome to a better solution.

Other approaches involve using arrays of real-valued numbers instead of bit strings to represent chromosomes. Results from the theory of schemata suggest that in general the smaller the alphabet, the better the performance, but it was initially surprising to researchers that good results were obtained from using real-valued chromosomes. This was explained as the set of real values in a finite population of chromosomes as forming a ''virtual alphabet'' (when selection and recombination are dominant) with a much lower cardinality than would be expected from a floating point representation.<ref name=Goldberg1991>{{cite book|last=Goldberg|first=David E.|title=Parallel Problem Solving from Nature|chapter=The theory of virtual alphabets|journal=Parallel Problem Solving from Nature, Lecture Notes in Computer Science|year=1991|volume=496|pages=13–22|doi=10.1007/BFb0029726|series=Lecture Notes in Computer Science|isbn=978-3-540-54148-6}}</ref><ref name=Janikow1991>{{cite journal|last1=Janikow|first1=C. Z.|first2=Z. |last2=Michalewicz |title=An Experimental Comparison of Binary and Floating Point Representations in Genetic Algorithms|journal=Proceedings of the Fourth International Conference on Genetic Algorithms|year=1991|pages=31–36|url=http://www.cs.umsl.edu/~janikow/publications/1991/GAbin/text.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.cs.umsl.edu/~janikow/publications/1991/GAbin/text.pdf |archive-date=2022-10-09 |url-status=live|access-date=2 July 2013}}</ref>

An expansion of the Genetic Algorithm accessible problem domain can be obtained through more complex encoding of the solution pools by concatenating several types of heterogenously encoded genes into one chromosome.<ref name=Patrascu2014>{{cite journal|last1=Patrascu|first1=M.|last2=Stancu|first2=A.F.|last3=Pop|first3=F.|title=HELGA: a heterogeneous encoding lifelike genetic algorithm for population evolution modeling and simulation|journal=Soft Computing|year=2014|volume=18|issue=12|pages=2565–2576|doi=10.1007/s00500-014-1401-y|s2cid=29821873}}</ref> This particular approach allows for solving optimization problems that require vastly disparate definition domains for the problem parameters. For instance, in problems of cascaded controller tuning, the internal loop controller structure can belong to a conventional regulator of three parameters, whereas the external loop could implement a linguistic controller (such as a fuzzy system) which has an inherently different description. This particular form of encoding requires a specialized crossover mechanism that recombines the chromosome by section, and it is a useful tool for the modelling and simulation of complex adaptive systems, especially evolution processes.

Another important expansion of the Genetic Algorithm (GA) accessible solution space was driven by the need to make representations amenable to variable levels of knowledge about the solution states. Variable-length representations were inspired by the observation that, in nature, evolution tends to progress from simpler organisms to more complex ones—suggesting an underlying rationale for embracing flexible structures.<ref>Goldberg, D.E., Korb, B., & Deb, K. (1989). Messy Genetic Algorithms: Motivation, Analysis, and First Results. Complex Systems, 3(5), 493–530. ISSN 0891-2513.</ref> A second, more pragmatic motivation was that most real-world engineering and knowledge-based problems do not naturally conform to rigid knowledge structures.<ref>Davidor, Y. (1991). Genetic Algorithms and Robotics: A Heuristic Strategy for Optimization. World Scientific Series in Robotics and Intelligent Systems: Volume 1.</ref>

These early innovations in variable-length representations laid essential groundwork for the development of [[Genetic programming]], which further extended the classical GA paradigm. Such representations required enhancements to the simplistic genetic operators used for fixed-length chromosomes, enabling the emergence of more sophisticated and adaptive GA models.