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：基准测试问题是理解优化算法的重要工具。由于算法通常旨在基准测试中表现良好，基准设计中的偏差会提供误导性见解。例如，在单目标优化中，许多问题的最优点曾位于搜索域中心。为解决这些问题，搜索空间变换已被基准测试套件广泛采用，以阻止算法利用非预期结构。在多目标优化中，问题设计主要聚焦于目标空间结构。尽管这一重点解决了多目标问题的重要方面，但这些问题中搜索空间结构受到的关注相对有限。在本工作中，我们重新强调搜索空间变换的重要性，并探讨如何在边界约束问题中添加变换而不影响目标空间结构中所固有的挑战。我们利用两种参数化双射变换，生成了流行基准测试问题的不同实例，并展示了这些变化如何影响多种多目标优化算法的性能。除搜索空间变换外，我们进一步表明此类参数化变换也可应用于目标空间，并比较了它们对性能的各自影响。