AI 中文总结
提出质量剖面图和测试集剖面图对优化算法基准测试，质量剖面图强调解准确性，通过数值实验展示其在光滑和非光滑优化中的作用，还提及绘制代码，以增强基准测试过程，评估测试集适用性。
AI 中文摘要
我们提出了几种用于对优化算法进行基准测试的新工具：质量剖面图和测试集剖面图。其目的是根据所得解的质量（即目标函数值）评估和比较算法，以及评估测试集的一致性。我们提出的质量剖面图的一个关键区别特征是其强调解的准确性的比较确定性过程，而非求解器的计算负担。本文还包括广泛的数值实验，展示了质量剖面图在光滑和非光滑（无导数）优化中的有用性，同时还提及了用于绘制质量剖面图和测试集剖面图的MATLAB代码。
英文摘要
We propose a couple of novel tools for benchmarking optimization algorithms which possibly converge to different solutions on a test set: the quality profiles and the test set profiles. Their aim is to assess and compare algorithms in terms of quality (i.e. value of the objective function) of the obtained solutions, as well as to assess the consistency of the test set. A key distinguishing feature of the quality profiles we propose is its comparative deterministic procedure that emphasizes the accuracy of the solution, rather than the computational burden of solvers. In this regard, several test set--dependent approaches for both comparing and ranking algorithms have already been proposed in the literature, representing widely used benchmarking procedures. We believe that the joint use of such procedures, along with the novel quality profiles detailed here, should enhance the benchmarking process, in all those cases where the comparison encompasses exact methods as well as heuristics. Moreover, the literature on numerical optimization seems to have paid less attention, in the last decade, to determining how appropriate a test set used for benchmarking the selected solvers may be. This motivates the introduction of test set profiles, which assess the appropriateness of a test set and represent the flip side of evaluating the robustness of the solvers on that test set. This paper also includes extensive numerical experiments, showing the usefulness of quality profiles in both smooth and nonsmooth (derivative--free) optimization, along with the reference to a MATLAB code for plotting quality profiles and test set profiles.
