论文标题
一个展示它们的图:在多目标景观中的有效集的可视化
One PLOT to Show Them All: Visualization of Efficient Sets in Multi-Objective Landscapes
论文作者
论文摘要
在研究中,连续多目标优化问题(MOP)的决策空间的可视化技术在研究中很少。长期以来,所有技术都集中在全球最优性上,甚至对于少数可用的景观可视化,例如成本景观,全球性是主要标准。相比之下,最近提出的梯度场热图(GFHS)强调了局部有效集的位置和吸引盆地,但忽略了解决方案质量方面集合的关系。 在本文中,我们提出了一种新的混合可视化技术,该技术结合了两种方法的优势,以便在单个可视化中代表局部和全局最优性。因此,我们以GFH方法为基础,但应用了一种新技术来近似局部高效点的位置,并将多目标梯度矢量场的差异用作强大的二阶条件。然后,确定的局部高效点的相对优势关系用于可视化MOP的完整景观。随着有关吸引力盆地的信息的增强,具有最佳权衡取舍(图)的景观图成为最有用的多目标景观可视化技术之一。
Visualization techniques for the decision space of continuous multi-objective optimization problems (MOPs) are rather scarce in research. For long, all techniques focused on global optimality and even for the few available landscape visualizations, e.g., cost landscapes, globality is the main criterion. In contrast, the recently proposed gradient field heatmaps (GFHs) emphasize the location and attraction basins of local efficient sets, but ignore the relation of sets in terms of solution quality. In this paper, we propose a new and hybrid visualization technique, which combines the advantages of both approaches in order to represent local and global optimality together within a single visualization. Therefore, we build on the GFH approach but apply a new technique for approximating the location of locally efficient points and using the divergence of the multi-objective gradient vector field as a robust second-order condition. Then, the relative dominance relationship of the determined locally efficient points is used to visualize the complete landscape of the MOP. Augmented by information on the basins of attraction, this Plot of Landscapes with Optimal Trade-offs (PLOT) becomes one of the most informative multi-objective landscape visualization techniques available.