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Conditions that Obviate the No-Free-Lunch Theorems for Optimization

机译:消除了非自由午餐定理进行优化的条件

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Roughly speaking, the no-free-lunch (NFL) theorems state that any blackbox algorithm has the same average performance as random search. These results have largely been ignored by algorithm researchers. This paper looks more closely at the NFL results and focuses on their implications for combinatorial problems typically faced by many researchers and practitioners. We derive necessary conditions for the NFL results to hold based on common problem structures. Often it is simple to verify that these conditions are not present in the class of problems under investigation, thus providing a theoretical basis for ignoring the doleful implications of NFL giving justification for believing there might be a dominant algorithm for the problem class under study. We apply our results to three common classes of problems. We find that only trivial subclasses of these problems fall under the NFL implications.
机译:粗略地说,无自由午餐(NFL)定理指出,任何黑盒算法均具有与随机搜索相同的平均性能。这些结果在很大程度上被算法研究人员所忽略。这篇论文更加仔细地研究了NFL的结果,重点关注了它们对许多研究人员和从业人员通常面临的组合问题的影响。我们基于常见问题结构得出NFL结果得以保持的必要条件。通常,很容易验证所研究的问题类别中不存在这些条件,从而为忽略NFL的负面影响提供了理论基础,从而有理由相信可能存在针对所研究问题类别的主导算法。我们将结果应用于三种常见的问题类别。我们发现,这些问题中只有琐碎的子类属于NFL的含义。

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