  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.
