Automated Algorithm Selection (AAS) is a popular meta-algorithmic approach and has demonstrated to work well for single-objective optimisation in combination with exploratory landscape features (ELA), i.e., (numerical) descriptive features derived from sampling the black-box (continuous) optimisation problem. In contrast to the abundance of features that describe single-objective optimisation problems, only a few features have been proposed for multi-objective optimisation so far. Building upon recent work on exploratory landscape features for box-constrained continuous multi-objective optimization problems, we propose a novel and complementary set of additional features (MO-ELA). These features are based on a random sample of points considering both the decision and objective space. The features are divided into 5 feature groups depending on how they are being calculated: non-dominated-sorting, descriptive statistics, principal component analysis, graph structures and gradient information. An AAS study conducted on well-established multi-objective benchmarks demonstrates that the proposed features contribute to successfully distinguishing between algorithm performance and thus adequately capture problem hardness resulting in models that come very close to the virtual best solver. After feature selection, the newly proposed features are frequently among the top contributors, underscoring their value in algorithm selection and problem characterisation.

翻译：自动化算法选择是一种流行的元算法方法，已证明在与探索性景观特征结合使用时，能很好地适用于单目标优化。探索性景观特征是通过对黑盒（连续）优化问题进行采样而得到的（数值）描述性特征。与描述单目标优化问题的丰富特征相比，迄今为止，为多目标优化提出的特征还很少。基于近期关于盒约束连续多目标优化问题的探索性景观特征的研究，我们提出了一组新颖且互补的附加特征集。这些特征基于一个同时考虑决策空间和目标空间的随机点样本。根据计算方式，这些特征被分为5个特征组：非支配排序、描述性统计、主成分分析、图结构和梯度信息。在成熟的多目标基准测试上进行的自动化算法选择研究表明，所提出的特征有助于成功区分算法性能，从而充分捕捉问题难度，产生的模型非常接近虚拟最佳求解器。经过特征选择后，新提出的特征经常位居贡献度前列，突显了它们在算法选择和问题表征中的价值。