Evolutionary algorithms have been successful in solving multi-objective optimization problems (MOPs). However, as a class of population-based search methodology, evolutionary algorithms require a large number of evaluations of the objective functions, preventing them from being applied to a wide range of expensive MOPs. To tackle the above challenge, this work proposes for the first time a diffusion model that can learn to perform evolutionary multi-objective search, called EmoDM. This is achieved by treating the reversed convergence process of evolutionary search as the forward diffusion and learn the noise distributions from previously solved evolutionary optimization tasks. The pre-trained EmoDM can then generate a set of non-dominated solutions for a new MOP by means of its reverse diffusion without further evolutionary search, thereby significantly reducing the required function evaluations. To enhance the scalability of EmoDM, a mutual entropy-based attention mechanism is introduced to capture the decision variables that are most important for the objectives. Experimental results demonstrate the competitiveness of EmoDM in terms of both the search performance and computational efficiency compared with state-of-the-art evolutionary algorithms in solving MOPs having up to 5000 decision variables. The pre-trained EmoDM is shown to generalize well to unseen problems, revealing its strong potential as a general and efficient MOP solver.

翻译：进化算法已成功应用于求解多目标优化问题（MOPs）。然而，作为一类基于种群的搜索方法，进化算法需要大量目标函数评估，这阻碍了其应用于广泛的昂贵MOPs场景。为应对上述挑战，本文首次提出一种能学习执行进化多目标搜索的扩散模型——EmoDM。该方法通过将进化搜索的逆向收敛过程视为前向扩散，从先前求解的进化优化任务中学习噪声分布。预训练的EmoDM可借助逆向扩散过程直接为新MOPs生成一组非支配解，而无需进一步执行进化搜索，从而显著减少所需函数评估次数。为增强EmoDM的可扩展性，本文引入基于互熵的注意力机制以捕获对目标最关键的决策变量。实验结果表明，在求解决策变量规模高达5000的MOPs时，EmoDM在搜索性能与计算效率方面均能与最先进进化算法相抗衡。预训练的EmoDM展现出对未见问题的良好泛化能力，凸显其作为通用高效MOP求解器的巨大潜力。