The inherent difficulty of solving a continuous, static, bound-constrained and single-objective black-box optimization problem depends on the characteristics of the problem’s fitness landscape and the algorithm being used. Exploratory landscape analysis (ELA) uses numerical features generated via a sampling process of the search space to describe such characteristics. Despite their success in a number of applications, these features have limitations related with the computational costs associated with generating accurate results. Consequently, only approximations are available in practice which may be unreliable, leading to systemic errors. The overarching aim of this paper is to evaluate the reliability of five well-known ELA feature sets across multiple dimensions and sample sizes. For this purpose, we propose a comprehensive experimental methodology combining exploratory and statistical validation stages, which uses resampling techniques to minimize the sampling cost, and statistical significance tests to identify strengths and weaknesses of individual features. The data resulting from the methodology is collected and made available in the LEarning and OPtimization Archive of Research Data v1.0. The results show that instances of the same function can have feature values that are significantly different; hence, non-generalizable across instances, due to the effects produced by the boundary constraints. In addition, some landscape features under evaluation are highly volatile, and strongly susceptible to changes in sample size. Finally, the results show evidence of a curse of modality, meaning that the sample size should increase with the number of local optima.

解决连续，静态，有界约束和单目标黑盒优化问题的固有困难取决于问题的适应度特征和所使用的算法。探索性景观分析（ELA）使用通过搜索空间采样过程生成的数字特征来描述此类特征。尽管它们在许多应用中取得了成功，但这些功能仍存在与生成精确结果相关的计算成本相关的限制。因此，实际上只有近似值是不可靠的，从而导致系统误差。本文的首要目标是评估多个维度和样本量下的五个著名的ELA功能集的可靠性。以此目的，我们提出了一种综合性的实验方法，该方法结合了探索性验证和统计验证阶段，该方法使用重采样技术以最小化采样成本，并使用统计显着性测试来识别各个功能的优缺点。该方法得出的数据已收集并提供给研究数据的学习和优化存档v1.0。结果表明，同一个函数的实例可以具有明显不同的特征值。因此，由于边界约束产生的影响，无法跨实例通用化。此外，正在评估的某些景观特征极易挥发，并且极易受到样本大小变化的影响。最后，结果显示出模态的诅咒，