Computational Complexity Analysis of Simple Genetic Programming On Two Problems Modeling Isolated Program Semantics

TL;DR

This paper initiates the theoretical analysis of genetic programming's computational complexity by examining simplified algorithms on two model problems, revealing key factors influencing their performance.

Contribution

It provides the first rigorous complexity analysis of genetic programming, emphasizing the effects of neutral moves and local mutation operators.

Findings

Neutral moves significantly impact algorithm efficiency.

Local mutation operators are crucial for performance.

Analysis offers insights into genetic programming design choices.

Abstract

Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming. We set up several simplified genetic programming algorithms and analyze them on two separable model problems, ORDER and MAJORITY, each of which captures an important facet of typical genetic programming problems. Both analyses give first rigorous insights on aspects of genetic programming design, highlighting in particular the impact of accepting or rejecting neutral moves and the importance of a local mutation operator.