Schema Theory for Genetic Programming with One-Point Crossover and Point Mutation

Abstract

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.

Evolutionary Discovery of Arbitrary Self-replicating Structures

“…The R-tree mutation operator simply picks an edge from the entire tree with uniform probability, and then eliminates the sub-tree below the edge. The R-tree encoding and genetic operators used allow CA rules to be constructed and evolved under a non-standard schema theorem similar to one proposed for genetic programming [8], even though R-trees do not represent conventional sequential programs.…”

Genetic Network Programming with Reinforcement Learning and Its Performance Evaluation

“…This procedure is defined as 1 step of GP. GP uses one-point crossover described in [11] and half-and-half initialization methods [8] for fixing the maximum depth of trees and producing trees with various sizes and shapes in an initial population. GP with ADFs has three ADFs in each individual.…”

Schema Disruption in Chromosomes That Are Structured as Binary Trees

“…Furthermore, we envision a population of chromosomes that all have the same shape. From within the GP community, the work that comes closest to our own efforts is that of Poli & Langdon [9]. Their definitions of schema, mutation, and crossover are the closest carryover to GP of the allied notions from standard GAs with linear bit arrangements.…”