Principled Design of Translation, Scale, and Rotation Invariant Variation Operators for Metaheuristics
This work addresses the need for more robust and automated operator design in metaheuristics, which is incremental as it builds on existing principles but introduces a novel automated method.
This paper tackled the problem of designing variation operators for metaheuristics that are robust across different optimization problems by investigating translation, scale, and rotation invariance, and proposed an automated approach to generate such operators. The results showed that the generated operators outperformed state-of-the-art ones on various complex problems with up to 1000 decision variables.
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.