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In the past three decades, a large number of metaheuristics have beenproposed and shown high performance in solving complex optimization problems.While most variation operators in existing metaheuristics are empiricallydesigned, this paper aims to design new operators automatically, which areexpected to be search space independent and thus exhibit robust performance ondifferent problems. For this purpose, this work first investigates theinfluence of translation invariance, scale invariance, and rotation invarianceon the search behavior and performance of some representative operators. Then,we deduce the generic form of translation, scale, and rotation invariantoperators. Afterwards, a principled approach is proposed for the automateddesign of operators, which searches for high-performance operators based on thededuced generic form. The experimental results demonstrate that the operatorsgenerated by the proposed approach outperform state-of-the-art ones on avariety of problems with complex landscapes and up to 1000 decision variables.

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