User-preference based multi-objective evolutionary algorithms (MOEAs) have attracted much attention recently because it helps save computational cost, make better use of the knowledge offered by the decision-maker, and offer more insight into solutions in the region of interest (ROI). Weight vectors based MOEAs can be converted to their user-preference based versions by offering a set of evenly distributed weight vectors located in ROI. Yet existing weight design methods can only generate weight vectors in the whole unit plane in the weight space. To generate an arbitrary number of weight vectors in ROI, this paper proposes a tri-objective user-preference based uniform weight design method using Delaunay Triangulation (PUWD-DT), so that weight vectors can be fine-tuned to uniformity in ROI. Furthermore, the proposed PUWD-DT based preference method with the achievement scalarizing function is assembled into MOEA/D to convert it into its user-preference based version (MOEA/D+PUWD-DT) and the convergence of population in ROI for optimization problems with irregular shaped Pareto front is also promoted. Finally, the MOEA/D+PUWD-DT is applied to the reservoir flood control operation problem, and our experimental results indicate that the proposed preference-based MOEA method performs better than the state-of-the-art.

基于用户偏好的多目标进化算法（MOEA）最近引起了很多关注，因为它有助于节省计算成本，更好地利用决策者提供的知识，并提供对感兴趣区域（ROI）解决方案的更多洞察）。通过提供一组位于 ROI 中的均匀分布的权重向量，可以将基于权重向量的 MOEA 转换为基于用户偏好的版本。而现有的权重设计方法只能在权重空间的整个单位平面上生成权重向量。为了在 ROI 中生成任意数量的权重向量，本文提出了一种基于三目标用户偏好的均匀权重设计方法，使用 Delaunay 三角剖分（PUWD-DT），以便权重向量可以在 ROI 中进行微调以保持均匀。此外，提出的具有成就标量函数的基于 PUWD-DT 的偏好方法被组装到 MOEA/D 中以将其转换为基于用户偏好的版本 (MOEA/D+PUWD-DT) 以及针对不规则优化问题的 ROI 中的种群收敛形帕累托前沿也得到推广。最后，将 MOEA/D+PUWD-DT 应用于水库防洪操作问题，我们的实验结果表明，所提出的基于偏好的 MOEA 方法的性能优于现有技术。