Stagnation in Evolutionary Algorithms: Convergence $\neq$ Optimality
This work addresses a foundational misconception in evolutionary algorithms, which could impact algorithm design and evaluation for researchers and practitioners in optimization.
The paper challenges the common belief in evolutionary computation that stagnation impedes convergence and that convergence implies optimality, showing through counterexamples that stagnation can facilitate population convergence and that convergence does not guarantee optimality.
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.