Semantic schema theory for genetic programming

2015 ◽  
Vol 44 (1) ◽  
pp. 67-87 ◽  
Author(s):  
Zahra Zojaji ◽  
Mohammad Mehdi Ebadzadeh
Keyword(s):  
Genetic Programming ◽  
Schema Theory ◽  
Semantic Schema

General Schema Theory for Genetic Programming with Subtree-Swapping Crossover: Part II

2003 ◽  
Vol 11 (2) ◽  
pp. 169-206 ◽  
Author(s):  
Riccardo Poli ◽  
Nicholas Freitag McPhee
Keyword(s):  
Genetic Programming ◽  
Schema Theory ◽  
Exact Formulation ◽  
Expected Number ◽  
Size Evolution ◽  
General Schema ◽  
Definition Of ◽  
Effective Fitness ◽  
Selection Of ◽  
Exact Definition

This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)). Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. The theory is based on a Cartesian node reference system, introduced in Part I, and on the notion of a variable-arity hyperschema, introduced here, which generalises previous definitions of a schema. The theory includes two main theorems describing the propagation of GP schemata: a microscopic and a macroscopic schema theorem. The microscopic version is applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. Therefore, this theorem is applicable to Koza's GP crossover with and without uniform selection of the crossover points, as well as one-point crossover, size-fair crossover, strongly-typed GP crossover, context-preserving crossover and many others. The macroscopic version is applicable to crossover operators in which the probability of selecting any two crossover points in the parents depends only on the parents' size and shape. In the paper we provide examples, we show how the theory can be specialised to specific crossover operators and we illustrate how it can be used to derive other general results. These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover.

Semantic schema modeling for genetic programming using clustering of building blocks

2017 ◽  
Vol 48 (6) ◽  
pp. 1442-1460 ◽  
Author(s):  
Zahra Zojaji ◽  
Mohammad Mehdi Ebadzadeh
Keyword(s):  
Genetic Programming ◽  
Building Blocks ◽  
Semantic Schema

An improved semantic schema modeling for genetic programming

2017 ◽  
Vol 22 (10) ◽  
pp. 3237-3260 ◽  
Author(s):  
Zahra Zojaji ◽  
Mohammad Mehdi Ebadzadeh
Keyword(s):  
Genetic Programming ◽  
Semantic Schema

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

1998 ◽  
Vol 6 (3) ◽  
pp. 231-252 ◽  
Author(s):  
Riccardo Poli ◽  
William B. Langdon
Keyword(s):  
Genetic Algorithms ◽  
Genetic Programming ◽  
Point Mutation ◽  
Schema Theory ◽  
Natural Counterpart ◽  
New Form ◽  
Definition Of ◽  
Original Concept

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.

General Schema Theory for Genetic Programming with Subtree-Swapping Crossover: Part I

2003 ◽  
Vol 11 (1) ◽  
pp. 53-66 ◽  
Author(s):  
Riccardo Poli ◽  
Nicholas Freitag McPhee
Keyword(s):  
Probability Distribution ◽  
Genetic Programming ◽  
Reference System ◽  
Schema Theory ◽  
General Schema ◽  
Selection Of

This is the first part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover. The theory is based on a Cartesian node reference system which makes it possible to describe programs as functions over the space N2 and allows one to model the process of selection of the crossover points of subtree-swapping crossovers as a probability distribution over N4. In Part I, we present these notions and models and show how they can be used to calculate useful quantities. In Part II we will show how this machinery, when integrated with other definitions, such as that of variable-arity hyperschema, can be used to construct a general and exact schema theory for the most commonly used types of GP

A View of Schema Theory

1997 ◽  
Vol 42 (2) ◽  
pp. 158-159
Author(s):  
Wayne D. Gray
Keyword(s):  
Schema Theory
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