The evaluation of heuristic optimizers on test problems, better known as \emph{benchmarking}, is a cornerstone of research in multi-objective optimization. However, most test problems used in benchmarking numerical multi-objective black-box optimizers come from one of two flawed approaches: On the one hand, problems are constructed manually, which result in problems with well-understood optimal solutions, but unrealistic properties and biases. On the other hand, more realistic and complex single-objective problems are composited into multi-objective problems, but with a lack of control and understanding of problem properties. This paper proposes an extensive problem generation approach for bi-objective numerical optimization problems consisting of the combination of theoretically well-understood convex-quadratic functions into unimodal and multimodal landscapes with and without global structure. It supports configuration of test problem properties, such as the number of decision variables, local optima, Pareto front shape, plateaus in the objective space, or degree of conditioning, while maintaining theoretical tractability: The optimal front can be approximated to an arbitrary degree of precision regarding Pareto-compliant performance indicators such as the hypervolume or the exact R2 indicator. To demonstrate the generator's capabilities, a test suite of 20 problem categories, called \emph{BONO-Bench}, is created and subsequently used as a basis of an illustrative benchmark study. Finally, the general approach underlying our proposed generator, together with the associated test suite, is publicly released in the Python package \texttt{bonobench} to facilitate reproducible benchmarking.

翻译：在测试问题上评估启发式优化器（通常称为基准测试）是多目标优化研究的基石。然而，用于评估数值多目标黑箱优化器的大多数测试问题都源自两种有缺陷的方法之一：一方面，手动构造的问题虽然具有易于理解的最优解，但往往具有不切实际的特性与偏差；另一方面，将更真实且复杂的单目标问题组合成多目标问题时，却缺乏对问题特性的控制与理解。本文提出了一种针对双目标数值优化问题的扩展问题生成方法，该方法通过组合理论上易于理解的凸二次函数，构建出具有或不具有全局结构的单峰与多峰景观。该方法支持配置测试问题的多种特性，例如决策变量数量、局部最优解数量、帕累托前沿形状、目标空间中的平台区域或条件数程度，同时保持理论上的可追踪性：对于符合帕累托准则的性能指标（如超体积或精确R2指标），其最优前沿可以近似到任意精度。为展示该生成器的能力，我们创建了一个包含20个问题类别的测试套件（称为BONO-Bench），并随后将其用作示例性基准研究的基础。最后，我们提出的生成器所基于的通用方法及其相关测试套件已在Python包bonobench中公开发布，以促进可复现的基准测试。