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

arXiv: https://arxiv.org/abs/2105.10657 · HTML: https://mlsanity.com/paper/2105.10657/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2021.

## Built on by (most cited first, 4 of 4)

- [Automated Design of Metaheuristic Algorithms: A Survey](https://mlsanity.com/paper/2303.06532/) (2023)
- [A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization](https://mlsanity.com/paper/2206.11526/) (2022)
- [Constrained Multi-objective Optimization with Deep Reinforcement Learning Assisted Operator Selection](https://mlsanity.com/paper/2402.12381/) (2024)
- [Deep Reinforcement Learning-Assisted Component Auto-Configuration of Differential Evolution Algorithm for Constrained Optimization: A Foundation Model](https://mlsanity.com/paper/2509.11016/) (2025)

## Abstract (arXiv)

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.