Dynamic multi-objective optimization with a changing number of objectives has recently attracted increasing attention due to its relevance to real-world problems whose evaluation criteria may evolve over time. However, existing benchmark test suites for this problem setting suffer from a fundamental limitation: when the number of objectives changes, the objective functions themselves also change implicitly. This makes it difficult to isolate and evaluate an algorithm's capability to handle dynamics in the number of objectives alone. In this paper, we analyze this issue in detail and show that several theoretical properties claimed in prior studies rely on an assumption that is violated by commonly used test suites. To address this problem, we propose a scalable benchmark test suite in which the objective functions are fixed throughout the optimization process, while the number of active objectives changes over time. Our benchmark is constructed by defining a maximum-objective problem and dynamically selecting subsets of objectives. To avoid degeneracy issues in classical DTLZ and WFG problems, we adopt Minus-DTLZ and Minus-WFG formulations, in which all objectives are mutually conflicting. Extensive benchmark studies using representative algorithms from the literature demonstrate the usefulness and flexibility of the proposed test suite.

翻译：近年来，由于实际问题的评估标准可能随时间演化，目标数量动态变化的多目标优化问题日益受到关注。然而，现有针对该问题场景的基准测试套件存在根本性缺陷：当目标数量改变时，目标函数本身也会随之隐式改变。这使得研究者难以单独评估算法应对目标数量动态变化的能力。本文深入分析了这一缺陷，并指出先前研究声称的若干理论性质依赖于一个被通用测试套件违反的假设。为解决此问题，我们提出一个可扩展基准测试套件，其中目标函数在整个优化过程中保持不变，而活跃目标的数量随时间动态变化。该基准通过定义最大目标问题并动态选择目标子集构建。为避免经典DTLZ和WFG问题中的退化问题，我们采用所有目标相互冲突的Minus-DTLZ和Minus-WFG公式。利用文献中代表性算法进行的大规模基准测试表明，本测试套件具有良好的实用性与灵活性。