Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical properties for the comparison of two methods on a given problem class. The proposed approach allows the experimenter to define desired levels of accuracy for estimates of mean performance differences on individual problem instances, as well as the desired statistical power for comparing mean performances over a problem class of interest. The method calculates the required number of problem instances, and runs the algorithms on each test instance so that the accuracy of the estimated differences in performance is controlled at the predefined level. Two examples illustrate the application of the proposed method, and its ability to achieve the desired statistical properties with a methodologically sound definition of the relevant sample sizes.

中文翻译：

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在算法的实验比较中估计样本量以提高功效和准确性

性能的实验比较代表了优化算法研究的重要方面。在这项工作中，我们提出了一种方法，该方法用于定义具有理想统计特性的实验设计所需的样本量，以比较给定问题类别上的两种方法。提出的方法允许实验者定义期望的准确度水平，以估计各个问题实例的平均性能差异，以及定义所需的统计功效，以比较感兴趣的问题类别上的平均性能。该方法计算所需数量的问题实例，并在每个测试实例上运行算法，以便将性能差异的估计值的精度控制在预定义的级别。有两个示例说明了该方法的应用，