Schema theory for genetic programming with one-point crossover and point mutation

We review the main results obtained in the theory of schemata in genetic programming (GP), emphasizing their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP, which is closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation, this concept of schema has been used to derive an improved schema theorem for GP that describes the propagation of schemata from one generation to the next. We discuss this result and show that our schema theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges.