Hands-On Genetic Algorithms with Python

The schema theorem

A more formal expression of the building-block hypothesis is Holland's schema theorem, also called the fundamental theorem of genetic algorithms.

This theorem refers to schemata (plural of schema), which are patterns (or templates) that can be found within the chromosomes. Each schema represents a subset of chromosomes that have a certain similarity among them.

For example, if the set of chromosomes is represented by binary strings of length four, the schema 1*01 represents all those chromosomes that have a 1 in the leftmost position, 01 in the rightmost two positions, and either a 1 or a 0 in the second from left position, since the * represents a wildcard value.

For each schema, we can assign two measurements:

• Order ...