Recently, Pareto Set Learning (PSL) has been proposed for learning the entire
Pareto set using a neural network. PSL employs preference vectors to scalarize
multiple objectives, facilitating the learning of mappings from preference
vectors to specific Pareto optimal solutions. Previous PSL methods have shown
their effectiveness in solving artificial multi-objective optimization problems
(MOPs) with uniform preference vector sampling. The quality of the learned
Pareto set is influenced by the sampling strategy of the preference vector, and
the sampling of the preference vector needs to be decided based on the Pareto
front shape. However, a fixed preference sampling strategy cannot
simultaneously adapt the Pareto front of multiple MOPs. To address this
limitation, this paper proposes an Evolutionary Preference Sampling (EPS)
strategy to efficiently sample preference vectors. Inspired by evolutionary
algorithms, we consider preference sampling as an evolutionary process to
generate preference vectors for neural network training. We integrate the EPS
strategy into five advanced PSL methods. Extensive experiments demonstrate that
our proposed method has a faster convergence speed than baseline algorithms on
7 testing problems. Our implementation is available at
this https URL

通过进化好性采样 (Evolutionary Preference Sampling，EPS) 策略，将其融入到五种高级 Pareto Set Learning (PSL) 方法中，该论文提出了一种有效的样本优先选择向量，实现了对 Pareto 集合的快速收敛速度。

进化偏好采样用于帕累托集学习

Evolutionary Preference Sampling for Pareto Set Learning

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.

提出使用扩散模型（EmoDM）解决演化多目标搜索的方法，通过学习先前解决的演化优化任务的噪声分布，在不经历进一步演化搜索的情况下，通过逆扩散生成一组非支配解，从而显著减少了所需的函数评估次数，并引入互信息熵注意机制来提高 EmoDM 的可伸缩性，实验证明 EmoDM 在解决具有多达 5000 个决策变量的 MOP 时在搜索性能和计算效率方面与最先进的演化算法相媲美，且 EmoDM 的预训练模型在未知问题上具有很好的泛化能力，展示了其作为通用高效 MOP 求解器的潜力。