Analyzing the Runtime of the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) on the Concatenated Trap Function

TL;DR

This paper provides the first runtime analysis of GOMEA on the concatenated trap function, demonstrating its efficiency and speedup over traditional algorithms by deriving an upper bound on its expected runtime.

Contribution

It introduces the first theoretical runtime bounds for GOMEA on a complex benchmark, highlighting its advantages over simpler evolutionary algorithms.

Findings

GOMEA can solve concatenated trap functions in polynomial time relative to problem parameters.

The derived runtime bound shows a significant speedup over (1+1) EA.

GOMEA effectively exploits problem structure through linkage learning.

Abstract

The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a state of the art evolutionary algorithm that leverages linkage learning to efficiently exploit problem structure. By identifying and preserving important building blocks during variation, GOMEA has shown promising performance on various optimization problems. In this paper, we provide the first runtime analysis of GOMEA on the concatenated trap function, a challenging benchmark problem that consists of multiple deceptive subfunctions. We derived an upper bound on the expected runtime of GOMEA with a truthful linkage model, showing that it can solve the problem in $O(m^{3}2^k)$ with high probability, where $m$ is the number of subfunctions and $k$ is the subfunction length. This is a significant speedup compared to the (1+1) EA, which requires $O(ln{(m)}(mk)^{k})$ expected evaluations.