Dynamic multi-objective optimization (DMOO) has recently attracted increasing interest from both academic researchers and engineering practitioners, as numerous real-world applications that evolve over time can be naturally formulated as dynamic multi-objective optimization problems (DMOPs). This growing trend necessitates advanced benchmarks for the rigorous evaluation of optimization algorithms under realistic conditions. This paper introduces a comprehensive and principled framework for constructing highly realistic and challenging DMOO benchmarks. The proposed framework features several novel components: 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. This work establishes a new standard for dynamic multi-objective optimization benchmarking, providing 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）近年来日益受到学术界与工程界的关注，因为许多随时间演化的实际应用可自然建模为动态多目标优化问题（DMOPs）。这一发展趋势亟需先进的基准测试体系，以便在真实场景下对优化算法进行严格评估。本文提出一个全面且原理化的框架，用于构建高度真实且具有挑战性的DMOO基准测试。该框架包含若干创新组件：允许帕累托最优解集在超曲面上演化的广义数学表述、通过可控变量贡献失衡生成异构景观的机制，以及引入时变变量交互与非可分离性的动态旋转矩阵。此外，我们整合了模拟不规则环境变化的时间扰动机制，并提出一种广义时间关联机制，系统地将历史解的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所提框架的有效性，其在真实性、复杂性及区分前沿算法性能方面均优于传统基准测试。本研究为动态多目标优化基准测试确立了新标准，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有力工具。