arXiv:2603.26749cs.NEcs.AI2026-03

无需训练的扩散模型动态优化,快速追踪变化中的最优解集。

Training-Free Diffusion-Driven Modeling of Pareto Set Evolution for Dynamic Multiobjective Optimization

  • 用解析式多步去噪机制,从历史解集生成新环境解。
  • 在CEC2018基准上收敛与多样性优于或媲美主流算法。
  • 适合对响应速度要求高、无法负担训练成本的场景。

动态多目标优化问题(DMOPs)具有随时间变化的目标函数,导致帕累托最优解集(POS)持续漂移,在有限响应时间内难以同时保持收敛性和多样性。现有基于预测的动态多目标进化算法(DMOEAs)要么依赖需大量训练的模型,要么采用单步种群映射,可能忽略POS演化的渐进性。本文提出DD-DMOEA,一种无需训练的扩散驱动型动态响应机制。核心思想是将前一环境获得的POS视为“噪声”样本集,通过解析构建的多步去噪过程引导其向当前最优解集演化。引入基于膝点的辅助策略指定新环境的目标区域,并推导显式概率密度公式以计算去噪更新,无需神经网络训练。为降低膝点预测误差带来的误导风险,设计不确定性感知机制,根据历史预测偏差自适应调整引导强度。在CEC2018动态多目标基准测试中,DD-DMOEA实现了竞争力或更优的收敛-多样性表现,并提供比多个前沿DMOEA更快的动态响应。

原文摘要 · Abstract (English)

Dynamic multiobjective optimization problems (DMOPs) feature time-varying objectives, which cause the Pareto optimal solution (POS) set to drift over time and make it difficult to maintain both convergence and diversity under limited response time. Many existing prediction-based dynamic multiobjective evolutionary algorithms (DMOEAs) either depend on learned models with nontrivial training cost or employ one-step population mapping, which may overlook the gradual nature of POS evolution. This paper proposes DD-DMOEA, a training-free diffusion-based dynamic response mechanism for DMOPs. The key idea is to treat the POS obtained in the previous environment as a "noisy" sample set and to guide its evolution toward the current POS through an analytically constructed multi-step denoising process. A knee-point-based auxiliary strategy is used to specify the target region in the new environment, and an explicit probability-density formulation is derived to compute the denoising update without neural training. To reduce the risk of misleading guidance caused by knee-point prediction errors, an uncertainty-aware scheme adaptively adjusts the guidance strength according to the historical prediction deviation. Experiments on the CEC2018 dynamic multiobjective benchmarks show that DD-DMOEA achieves competitive or better convergence-diversity performance and provides faster dynamic response than several state-of-the-art DMOEAs.

动态优化扩散模型多目标无训练

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