Knee-Based Decision Making and Visualization in Many-Objective Optimization

@article{9209056,
  author  = {He, Zhenan and Yen, Gary G. and Ding, Jinliang},
  journal = {IEEE Transactions on Evolutionary Computation},
  title   = {Knee-Based Decision Making and Visualization in Many-Objective Optimization},
  year    = {2021},
  volume  = {25},
  number  = {2},
  pages   = {292-306},
  doi     = {10.1109/TEVC.2020.3027620}
}

阅读目的

了解优化理论的前沿算法，了解贺喆南老师的当前工作，拓宽视野

词典

multiobjective optimization

many-objective optimization: 决策变量比 MOP 更多

Decision Maker

Pareto front

Pareto optimal solutions

SOI: Solution Of Interest

ROI: Region Of Interese

a posteriori: using the facts that you know now to from a judgement about what must have happened before

a priori: using previous experiences or facts to decide what the likely result of effect of something will be

interactive

achievement scalarizing function

简介

这是四川大学贺喆南老师发表在 IEEE TEVC 上的一篇文章，

摘要

摘要介绍了

引言

针对 multiobjective optimization problems 和 many-objective optimization problems，Multicriteria Decision Making 和 Evolutionary Multiobjective Optimization 的联合方法被广泛研究，以此引导 Decision Maker 探索目标空间中的 Solutions of Interest 或 Regions of Interest。

总结来说，有三种探索目标空间的方法

1. MCDM starts after the EMO process has ended.
2. the MCDM process starts before the EMO process does
3. both EMO and MCDM processes operate simultaneously

a posteriori

DMs are presented with hundreds or thousands of Pareto optimal solutions on a high-dimensional approximate Pareto front. It is claimed that DMs are usually not very good at handing large amounts of high-dimensional data and cannot deal with more than a few information items at a time.Therefore, it is believed very difficult to handle a large number of solutions by a posteriori approach.

a priori

On the other hand, in a priori means, the incorporation of preference before the search can bias the search toward the ROI and restrict the distribution of Pareto optimal solutions to a smaller part of Pareto front, which reduces the difficulty in solving MOPs and MaOPs in some degrees and simplifies the decision-making process.

However, in this condition, in order to express their preference clearly, DMs have to articulate their preference in mathematical forms or quantitative terms. Unfortunately, it is also hard for DMs to explicitly formulate their preference in the very beginning since DMs are typically more confident in qualitative judging and comparing than in quantitative explaining.

interactive

the interactive way progressively making DMs involved in the search and decision process, can relieve the above difficulties in looking for high-quality Pareto optimal solutions and expression of preference.

总结来说，a priori 方法适合在 DM 有明确目标的时候使用；否则，a posterior 和 interactive 方法应该更佳。

除此之外，和两个或三个变量的 MOP 相比，MaOP 中众多的目标让 EMO 估计 global Pareto front 更加困难，随着决策变量的增加，解的数量指数级增长，通用进化算法使用的选择机制很容易失效。

Furthermore，对低维度的 MOP 的可视化通过空间视觉关系能帮助决策，而在 MaOP 中高维空间可视化非常不直观甚至不可能。