Posterior Decision Making Based on Decomposition-Driven Knee Point Identification
提出一种简单有效的拐点识别方法，通过比较邻域内的局部权衡效用从一组折衷解中识别拐点，帮助决策者后验选择感兴趣的解，并在134个测试问题和两个工程问题上验证了性能。
Knee points, characterized as a small improvement on one objective can lead to a significant degradation on at least one of the other objectives, are attractive to decision makers (DMs) in multicriterion decision making. This article presents a simple and effective knee point identification (KPI) method to help DMs identify solution(s) of interest from a given set of tradeoff solutions thus facilitating posterior decision making. Our basic idea is to sequentially validate whether a solution is a knee point or not by comparing its localized tradeoff utility with others within its neighborhood characterized from a decomposition perspective. In particular, a solution is a knee point if and only if it has the best-localized tradeoff utility among its neighbors. We implement a GPU version that carries out the KPI in a parallel manner. This GPU version reduces the worst-case complexity from quadratic to linear. The performance of our proposed method is compared with five state-of-the-art KPI methods on 134 test problem instances and two real-world engineering design problems. Empirical results demonstrate its outstanding performance especially on problems with many local knee points. We further validate the usefulness of our proposed method for guiding evolutionary multiobjective optimization algorithms to search for knee points on the fly during the evolutionary process.