Schema (genetic algorithms)

In mathematics, in the field of genetic algorithms, a schema is a template that identifies a subset of strings with similarities at certain string positions. Schemata are a special case of cylinder sets; and so form a topological space.

Description

For example, consider binary strings of length 6. The schema 1**0*1 describes the set of all strings of length 6 with 1's at positions 1 and 6 and a 0 at position 4. 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 $\delta (H)$ 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.

See also

Holland's schema theorem

References

• Holland, Adaptation in Natural and Artificial Systems, The MIT Press; Reprint edition 1992 (originally published in 1975).