Exploratory landscape analysis and fitness landscape analysis in general have been pivotal in facilitating problem understanding, algorithm design and endeavors such as automated algorithm selection and configuration. These techniques have largely been limited to search spaces of a single domain. In this work, we provide the means to compute exploratory landscape features for mixed-variable problems where the decision space is a mixture of continuous, binary, integer, and categorical variables. This is achieved by utilizing existing encoding techniques originating from machine learning. We provide a comprehensive juxtaposition of the results based on these different techniques. To further highlight their merit for practical applications, we design and conduct an automated algorithm selection study based on a hyperparameter optimization benchmark suite. We derive a meaningful compartmentalization of these benchmark problems by clustering based on the used landscape features. The identified clusters mimic the behavior the used algorithms exhibit. Meaning, the different clusters have different best performing algorithms. Finally, our trained algorithm selector is able to close the gap between the single best and the virtual best solver by 57.5% over all benchmark problems.

翻译：探索性景观分析与适应性景观分析在促进问题理解、算法设计以及自动算法选择与配置等方面一直发挥着关键作用。这些技术主要局限于单一域的搜索空间。在本工作中，我们提出了为混合变量问题计算探索性景观特征的方法，其中决策空间由连续变量、二元变量、整数变量和分类变量混合构成。这一目标通过利用源自机器学习的现有编码技术得以实现。我们系统比较了基于这些不同技术所得结果。为进一步凸显其在实际应用中的价值，我们基于超参数优化基准测试套件设计并开展了一项自动算法选择研究。通过基于所用景观特征的聚类分析，我们得出了这些基准问题的有意义的划分。所识别的聚类反映了所用算法的表现行为，即不同聚类对应不同最佳性能算法。最终，我们训练的算法选择器在所有基准问题上将单一最优求解器与虚拟最优求解器之间的差距缩小了57.5%。