Denoising diffusion models (DDMs) offer a promising generative approach for combinatorial optimization, yet they often lack the robust exploration capabilities of traditional metaheuristics like evolutionary algorithms (EAs). We propose a Denoising Diffusion-based Evolutionary Algorithm (DDEA) framework that synergistically integrates these paradigms. It utilizes pre-trained DDMs for both high-quality and diverse population initialization and a novel diffusion-based recombination operator, trained via imitation learning against an optimal demonstrator. Evaluating DDEA on the Maximum Independent Set problem on Erd\H{o}s-R\'enyi graphs, we demonstrate notable improvements over DIFUSCO, a leading DDM solver. DDEA consistently outperforms it given the same time budget, and surpasses Gurobi on larger graphs under the same time limit, with DDEA's solution sizes being 3.9% and 7.5% larger on the ER-300-400 and ER-700-800 datasets, respectively. In out-of-distribution experiments, DDEA provides solutions of 11.6% higher quality than DIFUSCO under the same time limit. Ablation studies confirm that both diffusion initialization and recombination are crucial. Our work highlights the potential of hybridizing DDMs and EAs, offering a promising direction for the development of powerful machine learning solvers for complex combinatorial optimization problems.

翻译：去噪扩散模型为组合优化提供了一种有前景的生成式方法，但其通常缺乏如进化算法等传统元启发式算法所具有的鲁棒探索能力。本文提出一种基于去噪扩散的进化算法框架，该框架协同整合了这两种范式。它利用预训练的去噪扩散模型实现高质量且多样化的种群初始化，并引入一种基于扩散的新型重组算子，该算子通过模仿学习针对最优演示器进行训练。通过在Erdős-Rényi图上的最大独立集问题评估DDEA，我们证明了其相较于主流去噪扩散模型求解器DIFUSCO的显著改进。在相同时间预算下，DDEA始终优于DIFUSCO；在相同时间限制下，对于更大规模的图，DDEA超越了Gurobi求解器——在ER-300-400和ER-700-800数据集上，DDEA求得的解规模分别比Gurobi大3.9%和7.5%。在分布外实验中，相同时间限制下DDEA提供的解质量比DIFUSCO高11.6%。消融研究证实扩散初始化和重组操作均至关重要。我们的工作凸显了去噪扩散模型与进化算法融合的潜力，为开发针对复杂组合优化问题的强大机器学习求解器提供了有前景的研究方向。