Rowe Jon E, Vose M D, Wright Alden H
School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom.
Evol Comput. 2009 Spring;17(1):117-29. doi: 10.1162/evco.2009.17.1.117.
Abstract Since its inception, the "No Free Lunch" theorem (NFL) has concerned the application of symmetry results rather than the symmetries themselves. In our view, the conflation of result and application obscures the simplicity, generality, and power of the symmetries involved. This paper separates result from application, focusing on and clarifying the nature of underlying symmetries. The result is a general set-theoretic version of NFL which speaks to symmetries when arbitrary domains and co-domains are involved. Although our framework is deterministic, we note situations where our deterministic set-theoretic results speak nevertheless to stochastic algorithms.
摘要 自“没有免费的午餐”定理（NFL）提出以来，人们关注的一直是其对称性结果的应用，而非对称性本身。我们认为，将结果与应用混为一谈会掩盖所涉及对称性的简单性、普遍性和强大之处。本文将结果与应用区分开来，着重探讨并阐明潜在对称性的本质。由此得到了一个通用的集合论版本的NFL，它在涉及任意定义域和陪域时都能体现对称性。尽管我们的框架是确定性的，但我们也指出了一些情况，即我们的确定性集合论结果同样适用于随机算法。
