# 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}
}

## 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

## 引言¶

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.

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。