Computational Complexity Results for Genetic Programming and the Sorting Problem

TL;DR

This paper advances the theoretical understanding of genetic programming by analyzing its computational complexity on the sorting problem, focusing on dependent program semantics and different measures of sortedness.

Contribution

It extends prior work by providing a rigorous complexity analysis of GP on sorting with dependent semantics, a less-studied area.

Findings

GP can effectively handle various measures of sortedness

The analysis reveals the impact of dependent semantics on GP's performance

Results contribute to the theoretical foundation of GP for complex problems

Abstract

Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems with isolated program semantics. With this paper, we push forward the computational complexity analysis of GP on a problem with dependent program semantics. We study the well-known sorting problem in this context and analyze rigorously how GP can deal with different measures of sortedness.