Principled Design of Translation, Scale, and Rotation Invariant Variation Operators for Metaheuristics

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, new operators are automatically designed in this work, which are expected to be search space independent and thus exhibit robust performance on different problems. This work first investigates the influence of translation invariance, scale invariance, and rotation invariance on the search behavior and performance of some representative operators. This work then deduces the generic form of translation, scale, and rotation invariant operators, and proposes a principled approach 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.