The domain of metaheuristic optimization has become vibrant due to a flood of new algorithms using a new nature-inspired metaphor but lacking clear methodological novelty. The Criticism behind the development of these algorithms has reached such an extent that the critics started to assert that all novel algorithms are only copies of already developed ones. In this study, we try to show that the situation is not so black and white. Therefore, we define a strong equivalence theorem for estimating the similarity between two nature-inspired metaheuristics, according to which two algorithms are equivalent if, and only if, the cosine similarity of their phenotypic and genotypic feature vectors, characterizing their behavior by searching for the optimal solutions, is above some threshold. On the theorem basis, a framework is developed for identifying the equivalence between nature-inspired metaheuristics. Extensive experimental work using the framework has shown that searching for conditions to achieve the high similarity of the more well-known nature-inspired metaheuristics is hard, or even not possible to achieve, in the limited computational environments.

翻译：元启发式优化领域因大量使用新的自然启发隐喻但缺乏明确方法论创新的新算法而变得活跃。针对这些算法开发的批评已达到如此程度，以至于批评者开始断言所有新算法仅是已有算法的复制品。在本研究中，我们试图表明情况并非如此非黑即白。因此，我们定义了一个用于估计两种受自然启发的元启发式算法相似性的强等价定理，根据该定理，当且仅当表征其通过搜索最优解行为的表型和基因型特征向量的余弦相似度高于某个阈值时，两种算法才等价。基于该定理，开发了一个识别受自然启发的元启发式算法等价性的框架。使用该框架进行的广泛实验工作表明，在有限的计算环境中，寻找条件以实现更知名的受自然启发的元启发式算法的高相似性很困难，甚至不可能实现。