In the past three decades, a large number of metaheuristics have been proposed and shown high performance in solving complex optimization problems. While most variation operators in existing metaheuristics are empirically designed, this paper aims to design new operators automatically, which are expected to be search space independent and thus exhibit robust performance on different problems. For this purpose, this work first investigates the influence of translation invariance, scale invariance, and rotation invariance on the search behavior and performance of some representative operators. Then, we deduce the generic form of translation, scale, and rotation invariant operators. Afterwards, a principled approach is proposed for the automated design of operators, which searches for high-performance operators based on the deduced generic form. The experimental results demonstrate that the operators generated by the proposed approach outperform state-of-the-art ones on a variety of problems with complex landscapes and up to 1000 decision variables.

翻译：在过去三十年中,提出了大量计量经济学建议,并显示出在解决复杂的优化问题方面的高绩效。虽然现有计量经济学中的大多数不同操作员都是根据经验设计的,但本文件旨在自动设计新的操作员,预期这些操作员将独立搜索空间,从而在不同的问题上表现出强有力的表现。为此,这项工作首先调查翻译变换、规模变换和轮换对一些具有代表性的操作员的搜索行为和绩效的影响。然后,我们推断出翻译、规模和轮换变换操作员的通用形式。随后,为操作员的自动化设计提出了原则性做法,根据推断的通用形式寻找高性能操作员。实验结果表明,拟议方法所产生的操作员在复杂地貌和多达1,000个决定变量的各类问题上,超越了最先进的操作员。