Stagnation in Evolutionary Algorithms: Convergence $\neq$ Optimality

TL;DR

This paper challenges common beliefs in evolutionary algorithms by showing that stagnation can promote convergence without guaranteeing optimality, emphasizing the need for more nuanced analysis.

Contribution

It introduces the novel insight that individual stagnation can aid population convergence and that convergence does not imply optimality, supported by counterexamples.

Findings

Stagnation of individuals can facilitate overall convergence.

Convergence does not necessarily mean the solution is optimal.

Counterexamples demonstrate the disconnect between convergence and optimality.

Abstract

In the evolutionary computation community, it is widely believed that stagnation impedes convergence in evolutionary algorithms, and that convergence inherently indicates optimality. However, this perspective is misleading. In this study, it is the first to highlight that the stagnation of an individual can actually facilitate the convergence of the entire population, and convergence does not necessarily imply optimality, not even local optimality. Convergence alone is insufficient to ensure the effectiveness of evolutionary algorithms. Several counterexamples are provided to illustrate this argument.