绝对排名：基准测试优化算法的一种必要归一化方法
Absolute Ranking: An Essential Normalization for Benchmarking Optimization Algorithms
AI总结：
针对传统排名归一化会因新算法加入而改变原有排名的问题，本文提出 absolute ranking 数学模型及基于采样的计算方法，以提升跨算法、跨问题性能评估的稳健性。
摘要：
由于涉及的数值尺度多种多样，在许多问题上评估不同优化算法的性能是一项复杂挑战。传统数据处理方法（如假设检验和贝叶斯推断）常采用基于排名的方法，在这些变化尺度之间对性能值进行归一化。然而，这种基于排名的方法出现了一个重要问题：引入新算法可能会破坏原有排名。本文广泛探讨了这一问题，给出了有说服力的论据以强调该问题，并对其根本原因进行了深入分析。这些工作为全面考察可能的解决方案铺平了道路。在此研究基础上，本文提出了一种名为“absolute ranking（绝对排名）”的新数学模型，以及一种基于采样的计算方法。这些贡献还附带了实用的实施建议，旨在提供一个更稳健的框架，以解决在多种算法和问题之间评估性能时数值尺度变化的挑战。
英文摘要：
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference, often employ ranking-based methods to normalize performance values across these varying scales. However, a significant issue emerges with this ranking-based approach: the introduction of new algorithms can potentially disrupt the original rankings. This paper extensively explores the problem, making a compelling case to underscore the issue and conducting a thorough analysis of its root causes. These efforts pave the way for a comprehensive examination of potential solutions. Building on this research, this paper introduces a new mathematical model called "absolute ranking" and a sampling-based computational method. These contributions come with practical implementation recommendations, aimed at providing a more robust framework for addressing the challenge of numerical scale variation in the assessment of performance across multiple algorithms and problems.
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。
