Choosing a set of benchmark problems is often a key component of any empirical evaluation of iterative optimization heuristics. In continuous, single-objective optimization, several sets of problems have become widespread, including the well-established BBOB suite. While this suite is designed to enable rigorous benchmarking, it is also commonly used for testing methods such as algorithm selection, which the suite was never designed around. We present the MA-BBOB function generator, which uses the BBOB suite as component functions in an affine combination. In this work, we describe the full procedure to create these affine combinations and highlight the trade-offs of several design decisions, specifically the choice to place the optimum uniformly at random in the domain. We then illustrate how this generator can be used to gain more low-level insight into the function landscapes through the use of exploratory landscape analysis. Finally, we show a potential use-case of MA-BBOB in generating a wide set of training and testing data for algorithm selectors. Using this setup, we show that the basic scheme of using a set of landscape features to predict the best algorithm does not lead to optimal results, and that an algorithm selector trained purely on the BBOB functions generalizes poorly to the affine combinations.

翻译：选择基准问题集合通常是迭代优化启发式算法实证评估的关键组成部分。在连续单目标优化领域，多组基准问题已被广泛采用，其中包括久经考验的BBOB测试集。尽管该测试集旨在实现严谨的基准测试，但它也常被用于测试算法选择等方法——而这些并非该测试集的设计初衷。我们提出MA-BBOB问题生成器，该生成器将BBOB测试集作为仿射组合中的分量函数。本文详细阐述了构建这些仿射组合的完整流程，并重点分析了多项设计决策的权衡取舍，特别是将最优解随机均匀分布在定义域内的选择。随后我们展示了如何通过探索性景观分析，利用该生成器获取函数景观的更深层微观特征。最后，我们演示了MA-BBOB在生成算法选择器所需大规模训练与测试数据方面的潜在应用场景。通过该实验设置，我们发现：单纯依赖景观特征预测最优算法的基本方案无法获得最优结果，且仅基于BBOB函数训练的算法选择器对仿射组合问题的泛化能力较差。