Axiom schema of predicative separation: Difference between revisions

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A '''schema''' is a template in [[computer science]] used in the field of [[genetic algorithm]]s  that identifies a [[subset]] of strings with similarities at certain string positions. Schemata are a special case of [[cylinder set]]s; and so form a [[topological space]].<ref name="Holland1">{{cite book|last=Holland|title=Adaptation in Natural and Artificial Systems|year=1992 reprint|publisher=The MIT Press|author=Holland|accessdate=13 July 2010}}</ref>


== Description ==
For example, consider binary strings of length 6. The schema 1**0*1 describes the set of all words of length 6 with 1's at the first and sixth positions a 0 at the fourth position. The * is a [[Wildcard character|wildcard]] symbol, which means that positions 2, 3 and 5 can have a value of either 1 or 0. The ''order of a schema'' is defined as the number of fixed positions in the template, while the ''[[defining length]]'' <math> \delta(H) </math> is the distance between the first and last specific positions. The order of 1**0*1 is 3 and its defining length is 5. The ''fitness of a schema'' is the average fitness of all strings matching the schema. The fitness of a string is a measure of the value of the encoded problem solution, as computed by a problem-specific evaluation function.


===Length===
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The length of a schema <math>H</math>, called <math>N(H)</math>, is defined as the total number of nodes in the schema. <math>N(H)</math> is also equal to the number of nodes in the programs matching <math>H</math>.<ref name="UCL1">{{cite web|title=Foundations of Genetic Programming|url=http://www.cs.ucl.ac.uk/staff/W.Langdon/FOGP/|publisher=UCL UK|accessdate=13 July 2010}}</ref>
 
===Disruption===
If the child of an individual that matches schema H does not ''itself'' match H, the schema is said to have been ''disrupted''.<ref name="UCL1"></ref>
 
==See also==
*[[Holland's schema theorem]]
*[[Propagation of schema]]
 
==References==
{{Reflist}}
 
{{bioinformatics-stub}}
{{compu-AI-stub}}
{{comp-sci-stub}}
 
[[Category:Genetic algorithms]]
[[Category:Genetic programming]]

Latest revision as of 21:20, 25 September 2014


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