50.174.221.28: Fix for mathjax - \exist -> \exists

2014-09-25T19:20:04Z

Fix for mathjax - \exist -> \exists

← Older revision		Revision as of 21:20, 25 September 2014
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	~~{{merge from\|Propagation of schema\|date=December 2011}}~~
	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*01 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*01 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.

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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]~~]

en>Gabbe: changed hyphens to dashes per WP:ENDASH

2012-08-21T20:57:20Z

changed hyphens to dashes per WP:ENDASH

New page

{{merge from|Propagation of schema|date=December 2011}}
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===
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]]

Axiom schema of predicative separation - Revision history

50.174.221.28: Fix for mathjax - \exist -> \exists

en>Gabbe: changed hyphens to dashes per WP:ENDASH