Real-world black-box optimization often involves time-consuming or costly experiments and simulations. Multi-fidelity optimization (MFO) stands out as a cost-effective strategy that balances high-fidelity accuracy with computational efficiency through a hierarchical fidelity approach. This survey presents a systematic exploration of MFO, underpinned by a novel text mining framework based on a pre-trained language model. We delve deep into the foundational principles and methodologies of MFO, focusing on three core components -- multi-fidelity surrogate models, fidelity management strategies, and optimization techniques. Additionally, this survey highlights the diverse applications of MFO across several key domains, including machine learning, engineering design optimization, and scientific discovery, showcasing the adaptability and effectiveness of MFO in tackling complex computational challenges. Furthermore, we also envision several emerging challenges and prospects in the MFO landscape, spanning scalability, the composition of lower fidelities, and the integration of human-in-the-loop approaches at the algorithmic level. We also address critical issues related to benchmarking and the advancement of open science within the MFO community. Overall, this survey aims to catalyze further research and foster collaborations in MFO, setting the stage for future innovations and breakthroughs in the field.

翻译：现实世界的黑箱优化往往涉及耗时或昂贵的实验与仿真。多保真度优化（MFO）作为一种成本效益显著的策略，通过分层次保真度方法，在高保真精度与计算效率之间实现了平衡。本综述基于预训练语言模型的新型文本挖掘框架，对MFO进行了系统性的探索。我们深入研究了MFO的基础原理与方法论，重点关注三大核心组成——多保真度代理模型、保真度管理策略与优化技术。此外，本综述还突出展示了MFO在机器学习、工程设计优化和科学发现等多个关键领域的多样化应用，彰显了MFO在应对复杂计算挑战中的适应性与有效性。同时，我们展望了MFO领域出现的若干挑战与前景，涵盖可扩展性、低保真度组合，以及在算法层面集成人在回路的方法等问题。我们还讨论了与基准测试和推动MFO社区开放科学相关的关键议题。总体而言，本综述旨在促进MFO领域的进一步研究与协作，为该领域的未来创新与突破奠定基础。