机器学习优化算法与元启发式算法的315个基准与测试函数综述：含数学与可视化描述
A Review of 315 Benchmark and Test Functions for Machine Learning Optimization Algorithms and Metaheuristics with Mathematical and Visual Descriptions
AI总结：
该综述系统梳理300多个优化与元启发式基准测试函数，按特征和性质编目，总结25个常用函数并提出两个高维动态新函数，同时指出基准测试差距与未来方向。
摘要：
在快速发展的优化与元启发式领域，算法的效能在很大程度上由基准（测试）函数决定。尽管过去几十年中已经开发并推导了许多函数，但关于其中许多函数的数学与可视化描述、适用范围以及应用，现有信息仍然很少。为弥合这一知识空白，本综述对用于评估优化和元启发式算法的300多个基准函数进行了详尽调研。本综述首先依据基准与测试函数的特征、复杂性、性质、可视化结果和领域影响对其进行分类编目，以提供广阔视角，帮助针对各种算法挑战选择合适的基准。本综述还列出了公开文献中最常用的25个函数，并提出了两个新的高维、动态且具有挑战性的函数，可用于测试新算法。最后，本综述指出了当前基准测试实践中的不足，并为未来研究提出了方向。
英文摘要：
In the rapidly evolving optimization and metaheuristics domains, the efficacy of algorithms is crucially determined by the benchmark (test) functions. While several functions have been developed and derived over the past decades, little information is available on the mathematical and visual description, range of suitability, and applications of many such functions. To bridge this knowledge gap, this review provides an exhaustive survey of more than 300 benchmark functions used in the evaluation of optimization and metaheuristics algorithms. This review first catalogs benchmark and test functions based on their characteristics, complexity, properties, visuals, and domain implications to offer a wide view that aids in selecting appropriate benchmarks for various algorithmic challenges. This review also lists the 25 most commonly used functions in the open literature and proposes two new, highly dimensional, dynamic and challenging functions that could be used for testing new algorithms. Finally, this review identifies gaps in current benchmarking practices and suggests directions for future research.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
