逗号选择在带有随机植入最优解的 OneMax 上优于加号选择
Comma Selection Outperforms Plus Selection on OneMax with Randomly Planted Optima
AI总结：
本文提出带冻结噪声随机植入局部最优的 OneMax 基准，证明固定目标下 (1,λ) EA 可比 (1+λ) EA 快至 Θ(n ln n) 倍，并给出带尾界的通用分析方法。
摘要：
进化算法中的逗号选择是否以及如何帮助逃离局部最优，一直存在争论。我们提出一种新的基准函数来研究逗号选择的优势：带有由冻结噪声生成的随机植入局部最优的 OneMax。我们证明，在固定目标场景下，以及在两种算法表现不同的子代种群规模 λ 下，逗号选择（(1,λ) EA）在该基准上快于加号选择（(1+λ) EA）。对于某些参数，(1,λ) EA 以高概率（w.h.p.）在 Θ(n ln n) 次评估内找到目标，而 (1+λ) EA 以高概率几乎需要 Θ((n ln n)^2) 次评估。我们进一步证明，逗号选择的优势并非任意大：对于大多数合理的参数选择，以高概率其优于加号选择的倍数至多为 O(n ln n)。我们开发了分析冻结噪声的新方法，并给出了强大且通用的固定目标结果及尾界，这些结果本身也具有独立价值。
英文摘要：
It is an ongoing debate whether and how comma selection in evolutionary algorithms helps to escape local optima. We propose a new benchmark function to investigate the benefits of comma selection: OneMax with randomly planted local optima, generated by frozen noise. We show that comma selection (the $(1,λ)$ EA) is faster than plus selection (the $(1+λ)$ EA) on this benchmark, in a fixed-target scenario, and for offspring population sizes $λ$ for which both algorithms behave differently. For certain parameters, the $(1,λ)$ EA finds the target in $Θ(n \ln n)$ evaluations, with high probability (w.h.p.), while the $(1+λ)$ EA) w.h.p. requires almost $Θ((n\ln n)^2)$ evaluations. We further show that the advantage of comma selection is not arbitrarily large: w.h.p. comma selection outperforms plus selection at most by a factor of $O(n \ln n)$ for most reasonable parameter choices. We develop novel methods for analysing frozen noise and give powerful and general fixed-target results with tail bounds that are of independent interest.
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。
