The performance of automated algorithm selection (AAS) strongly depends on the portfolio of algorithms to choose from. Selecting the portfolio is a non-trivial task that requires balancing the trade-off between the higher flexibility of large portfolios with the increased complexity of the AAS task. In practice, probably the most common way to choose the algorithms for the portfolio is a greedy selection of the algorithms that perform well in some reference tasks of interest. We set out in this work to investigate alternative, data-driven portfolio selection techniques. Our proposed method creates algorithm behavior meta-representations, constructs a graph from a set of algorithms based on their meta-representation similarity, and applies a graph algorithm to select a final portfolio of diverse, representative, and non-redundant algorithms. We evaluate two distinct meta-representation techniques (SHAP and performance2vec) for selecting complementary portfolios from a total of 324 different variants of CMA-ES for the task of optimizing the BBOB single-objective problems in dimensionalities 5 and 30 with different cut-off budgets. We test two types of portfolios: one related to overall algorithm behavior and the `personalized' one (related to algorithm behavior per each problem separately). We observe that the approach built on the performance2vec-based representations favors small portfolios with negligible error in the AAS task relative to the virtual best solver from the selected portfolio, whereas the portfolios built from the SHAP-based representations gain from higher flexibility at the cost of decreased performance of the AAS. Across most considered scenarios, personalized portfolios yield comparable or slightly better performance than the classical greedy approach. They outperform the full portfolio in all scenarios.

翻译：自动算法选择（AAS）的性能强烈依赖于可供选择的算法投资组合。选取投资组合是一项非平凡任务，需要在大型投资组合的更高灵活性与AAS任务复杂度增加之间权衡取舍。实践中，最常见的投资组合构建方法可能是贪婪选择在若干相关参考任务中表现优异的算法。本研究旨在探索替代性的数据驱动投资组合选择技术。我们提出的方法通过构建算法行为元表示，基于元表示相似度从算法集合中构建图，并应用图算法选择由多样性、代表性及非冗余算法组成的最终投资组合。我们评估了两种不同的元表示技术（SHAP和performance2vec），用于从总共324个CMA-ES变体中为5维和30维BBOB单目标优化任务（采用不同截断预算）选取互补性投资组合。我们测试了两类投资组合：一类基于全局算法行为，另一类为"个性化"投资组合（针对每个问题单独考虑算法行为）。观察到基于performance2vec表示的方法倾向于选择小型投资组合，且相对于所选投资组合中的虚拟最优求解器，其AAS任务误差可忽略不计；而基于SHAP表示构建的投资组合通过降低AAS性能为代价获得了更高灵活性。在多数测试场景中，个性化投资组合的性能与经典贪婪方法相当或略优，并在所有场景中均优于全量投资组合。