The field of Dynamic Multi-Objective Optimization (DMOO) has witnessed a surge of interest from both academia and industry, as numerous time-evolving real-world applications can be naturally formulated as Dynamic Multi-Objective Optimization Problems (DMOPs). This growing demand thus necessitates advanced benchmarks to rigorously evaluate optimization algorithms under realistic conditions. This paper introduces a comprehensive and principled framework for constructing highly realistic and challenging DMOO benchmarks. The proposed framework incorporates several novel components, including: a generalized formulation that allows the Pareto-optimal Set (PS) to change on hypersurfaces; a mechanism for creating controlled variable contribution imbalances to generate heterogeneous landscapes; and dynamic rotation matrices for inducing time-varying variable interactions and non-separability. Furthermore, we incorporate a temporal perturbation mechanism to simulate irregular environmental changes and propose a generalized time-linkage mechanism that systematically embeds historical solution quality into future problems, thereby capturing critical real-world phenomena such as error accumulation and time-deception. Extensive experimental results validate the effectiveness of the proposed framework, demonstrating its superiority over conventional benchmarks in terms of realism, complexity, and its capability for discriminating state-of-the-art algorithmic performance. Thus, this work establishes a new standard for dynamic multi-objective optimization benchmarking and provides a powerful tool for the development and evaluation of next-generation algorithms capable of addressing the complexities of real-world dynamic systems.

翻译：动态多目标优化（DMOO）领域已引起学术界和工业界的广泛关注，因为许多随时间演变的实际应用问题可自然建模为动态多目标优化问题（DMOPs）。这一日益增长的需求要求建立先进的基准测试，以便在现实条件下严格评估优化算法。本文提出一个全面且原则性的框架，用于构建高度真实且富有挑战性的DMOO基准测试。该框架包含多个创新组件：允许帕累托最优集（PS）在超曲面上变化的通用化表述；创建可控变量贡献不平衡以生成异质景观的机制；以及用于诱导时变变量交互与非可分离性的动态旋转矩阵。此外，我们引入时间扰动机制模拟非规则环境变化，并提出一种广义时间关联机制，系统地将历史解质量嵌入未来问题中，从而捕捉误差累积与时间欺骗等关键现实现象。大量实验结果验证了该框架的有效性，证明其在真实性、复杂度以及对最先进算法性能的区分能力上优于传统基准测试。因此，本研究为动态多目标优化基准测试建立了新标准，并为开发与评估能够应对现实动态系统复杂性的下一代算法提供了强大工具。