Schema (genetic algorithms)

: schemata) is a template in computer science used in the field of genetic algorithms that identifies a subset of strings with similarities at certain string positions.

Schemata are a special case of cylinder sets, forming a basis for a product topology on strings.

[1] In other words, schemata can be used to generate a topology on a space of strings.

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 and a 0 at the fourth position.

The * is a 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

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.

, is defined as the total number of nodes in the schema.

is also equal to the number of nodes in the programs matching

[2] If the child of an individual that matches schema H does not itself match H, the schema is said to have been disrupted.

[2] In evolutionary computing such as genetic algorithms and genetic programming, propagation refers to the inheritance of characteristics of one generation by the next.

Those in the next generation may be (but do not have to be) children of parents who matched it.

Recently schema have been studied using order theory.

[3] Two basic operators are defined for schema: expansion and compression.

The expansion maps a schema onto a set of words which it represents, while the compression maps a set of words on to a schema.

denotes all words of length

denotes all schema of length

denotes the character at position

One can think of this operator as stacking up all the items in

and if all elements in a column are equivalent, the symbol at that position in

takes this value, otherwise there is a wild card symbol.

Schemata can be partially ordered.

is a partial ordering on a set of schemata from the reflexivity, antisymmetry and transitivity of the subset relation.

The compression and expansion operators form a Galois connection, where

, we call the process of calculating the compression on each subset of A, that is

The schematic lattice is similar to the concept lattice found in Formal concept analysis.