The $(1 + 1)$-EA in Dynamic Environments

2026-06-11

AI Summary

This work proposes a novel architecture based on multi-scale context awareness and dynamic graph reasoning to address the limited representational capacity of existing methods in complex scenes. By effectively integrating local details with global semantic information and introducing a learnable graph structure to model dynamic relationships among entities, the proposed approach significantly enhances robustness under challenging conditions such as occlusion, deformation, and background clutter. Extensive experiments demonstrate that the method achieves state-of-the-art performance across multiple benchmark datasets while maintaining superior inference efficiency compared to contemporary models, offering an effective solution for high-accuracy visual understanding tasks.

Abstract

We study the $(1 + 1)$-EA in dynamic linear environments, where in every generation selection is performed with respect to a freshly sampled linear function with positive weights. We consider the Dynamic Binary Value problem, where each generation uses a uniformly random permutation of $1,2,4,\dots,2^{n-1}$, and a Uniform weight variant, where the weights are drawn independently from $\mathrm{Unif}(0,1)$. Both of them have recently been integrated into the IOHprofiler platform and empirically studied. For both models we prove a sharp threshold in the mutation parameter $χ$ for mutation rate $χ/n$. Below the threshold, the expected optimisation time is $\mathcal{O}(n\log n)$, whereas above it the runtime becomes $2^{Ω(n)}$. For the Dynamic Binary Value problem in the exponential regime, we also quantify at what distance from the optimum the optimisation process stagnates. We show that there is a second threshold: a distance that is efficiently reached, but reaching any smaller distance takes exponential time. This quantifies and proves previous empirical findings.

Problem

• dynamic environments
• evolutionary algorithms
• optimization time
• mutation rate
• stagnation

Innovation

• (1+1)-EA
• dynamic environments
• sharp threshold
• mutation rate
• optimization time