Evolutionary Algorithms Are Significantly More Robust to Noise When They Ignore It

TL;DR

This paper demonstrates that evolutionary algorithms can be more robust to noise when they ignore it, challenging the common assumption that re-evaluations are necessary for robustness in noisy optimization problems.

Contribution

First mathematical analysis showing that a simple evolutionary algorithm without re-evaluations outperforms re-evaluation strategies under certain noise conditions.

Findings

EA without re-evaluations can optimize LeadingOnes with constant noise rates

Re-evaluations are less necessary and can be detrimental in noisy optimization

Results likely extend to other classic benchmarks

Abstract

Randomized search heuristics (RSHs) are known to have a certain robustness to noise. Mathematical analyses trying to quantify rigorously how robust RSHs are to a noisy access to the objective function typically assume that each solution is re-evaluated whenever it is compared to others. This aims at preventing that a single noisy evaluation has a lasting negative effect, but is computationally expensive and requires the user to foresee that noise is present (as in a noise-free setting, one would never re-evaluate solutions). In this work, we conduct the first mathematical runtime analysis of an evolutionary algorithm solving a single-objective noisy problem without re-evaluations. We prove that the $(1+1)$ evolutionary algorithm without re-evaluations can optimize the classic LeadingOnes benchmark with up to constant noise rates, in sharp contrast to the version with re-evaluations, where only noise with rates $O(n^{-2} \log n)$ can be tolerated. This result suggests that re-evaluations are much less needed than what was previously thought, and that they actually can be highly detrimental. The insights from our mathematical proofs indicate that this similar results are plausible for other classic benchmarks.