ABSTRACT
This chapter describes that for a GA incorporating jumping gene (JG) operations, the exact schema formulae for selection, crossover, and mutation can be directly borrowed from the ones derived by Stephens and Waelbroeck. To study a scheme, two of its attributes are of importance. One is called the order of a schema o(ξ), representing the number of actual bits in the schema. The next is the defining length of a schema, denoted Ld(ξ), defined as the distance between the leftmost and the rightmost actual bits. Holland schema theorem predicts the expected number of strings belonging to a schema in a population being evolved from one generation to the next, under the operations of selection, one-point crossover, and bit mutation. To further improve Holland's model, Stephens and Waelbroeck derived a new schema evolution equation that gave an exact formulation for selection, single-point crossover, and mutation.
