Computational Complexity Analysis of Multi-Objective Genetic Programming

TL;DR

This paper analyzes how incorporating syntax tree complexity as a secondary criterion affects the runtime and Pareto front computation in multi-objective genetic programming, extending prior simple problem analyses.

Contribution

It introduces a complexity-aware multi-criteria fitness function and analyzes its impact on the computational complexity of GP algorithms.

Findings

Complexity as a secondary criterion influences runtime behavior.

Expected time to compute Pareto front is analyzed for multi-objective GP.

Generalizations of ORDER and MAJORITY are studied.

Abstract

The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences the runtime behavior. We consider generalizations of ORDER and MAJORITY and present a computational complexity analysis of (1+1) GP using multi-criteria fitness functions that take into account the original objective and the complexity of a syntax tree as a secondary measure. Furthermore, we study the expected time until population-based multi-objective genetic programming algorithms have computed the Pareto front when taking the complexity of a syntax tree as an equally important objective.