Benchmark problems are an important tool for gaining understanding of optimization algorithms. Since algorithms often aim to perform well on benchmarks, biases in benchmark design provide misleading insights. In single-objective optimization, for example, many problems used to have their optimum in the center of the search domain. To remedy these issues, search space transformations have been widely adopted by benchmark suites, preventing algorithms from exploiting unintended structure. In multi-objective optimization, problem design has focused primarily on the objective space structure. While this focus addresses important aspects of the multi-objective nature of the problems, the search space structures of these problems have received comparatively limited attention. In this work, we re-emphasize the importance of transformations in the search space, and address the challenges inherent in adding transformations to boundary constraints problems without impacting the structure of the objective space. We utilized two parameterized, bijective transformations to create different instantiations of popular benchmark problems, and show how these changes impact the performance of various multi-objective optimization algorithms. In addition to the search space transformations, we show that such parameterized transformations can also be applied to the objective space, and compare their respective performance impacts.

翻译：基准问题作为理解优化算法的重要工具，在实际应用中具有关键价值。由于算法通常旨在基准问题上取得优异表现，基准设计中的偏差会引发误导性认知。以单目标优化为例，许多问题曾将最优解设置在搜索域中心。为消除此类问题，搜索空间变换已被基准测试集广泛采用，以防止算法利用非预期的结构特征。在多目标优化中，问题设计主要聚焦于目标空间结构。尽管这种关注解决了问题多目标特性的重要方面，但搜索空间结构所受的关注相对有限。本文重新强调搜索空间变换的重要性，并探讨在边界约束问题中添加变换时不影响目标空间结构面临的固有挑战。我们采用两种参数化双射变换，对主流基准问题生成不同实例，揭示这些变化对多种多目标优化算法性能的影响。除搜索空间变换外，我们还展示了此类参数化变换同样可应用于目标空间，并比较了它们各自对性能的影响。