Differential Evolution (DE) is a widely used evolutionary algorithm for black-box optimization problems. However, in modern DE implementations, a major challenge lies in the limited population diversity caused by the fixed population size enforced by the generational replacement. Population size is a critical control parameter that significantly affects DE performance. Larger populations inherently contain a more diverse set of individuals, thereby facilitating broader exploration of the search space. Conversely, when the maximum evaluation budgets is constrained, smaller populations focusing on a limited number of promising candidates may be more suitable. Many state-of-the-art DE variants incorporate an archive mechanism, in which a subset of discarded individuals is preserved in an archive during generation replacement and reused in mutation operations. However, maintaining what is essentially a secondary population via an archive introduces additional design considerations, such as policies for insertion, deletion, and appropriate sizing. To address these limitations, we propose a novel DE framework called Unbounded Differential Evolution (UDE), which adds all generated candidates to the population without discarding any individual based on fitness. Unlike conventional DE, which removes inferior individuals during generational replacement, UDE eliminates replacement altogether, along with the associated complexities of archive management and dynamic population sizing. UDE represents a fundamentally new approach to DE, relying solely on selection mechanisms and enabling a more straightforward yet powerful search algorithm.

翻译：差分进化（DE）是一种广泛应用于黑盒优化问题的进化算法。然而，在现代DE实现中，一个主要挑战在于由代际替换所强制执行的固定种群规模导致的有限种群多样性。种群规模是一个关键的控制参数，显著影响DE的性能。较大的种群本质上包含更多样化的个体，从而有助于更广泛地探索搜索空间。反之，当最大评估预算受限时，专注于有限数量有希望候选解的较小种群可能更为合适。许多先进的DE变体采用了存档机制，即在代际替换过程中将一部分被淘汰的个体保存在存档中，并在变异操作中重新使用。然而，通过存档维护本质上是一个次级种群会引入额外的设计考虑，例如插入、删除策略以及适当的规模设定。为解决这些局限性，我们提出了一种称为无界差分进化（UDE）的新型DE框架，该框架将所有生成的候选解添加到种群中，而不基于适应度丢弃任何个体。与在代际替换过程中移除劣势个体的传统DE不同，UDE完全取消了替换操作，同时避免了与之相关的存档管理和动态种群规模调整的复杂性。UDE代表了一种根本性的DE新方法，它仅依赖于选择机制，从而实现了一种更直接且强大的搜索算法。