多目标优化Knee前沿搜索方法研究进展

A study of multi-objective optimization:focus on Knee

多目标优化算法是近年来进化计算研究领域的一个热点,大多数的多目标优化算法试图找到问题的完整的Pareto前沿.然而,随着待优化问题目标个数的增加,算法需要更大的种群规模才能合理地描绘出完整的Pareto前沿.显然这样不仅增加了算法的运行时间,更增加了(决策者)最终解的选择难度.因此,聚焦于搜索Pareto前沿上的特定区域显得尤为重要,近年来也得到了越来越多学者的关注.Knee点指的是Pareto前沿上具有最大边际效用的点,在这个点附近,一个目标值的微小提升将带来至少一个其他目标值的巨大衰退,因此该点通常被认为是在没有特殊偏好的情况下对决策者更具吸引力的点.本文旨在对多目标优化中Knee前沿搜索相关的方法进行总结,包括Knee的检测方法、保留策略、测试问题等,并对多目标优化的Knee前沿搜索未来研究工作进行展望.

Multi-objective optimization algorithms(MOEAs)have been a hot spot in the field of evolutionary computation in recent years.Most MOEAs try to find the whole Pareto front of the problem.However,as the number of objectives increases,the algorithm requires a larger population to reasonably describe the whole Pareto front.Obviously,this not only increases the running time of the algorithm,but also increases the difficulty of selecting the final solution.Therefore,it is particularly important to focus on searching a specific area on the Pareto front,which has also attracted the attention of more and more scholars.The Knee point refers to the point with the greatest marginal utility on the Pareto front.Near this point,a small increase of an objective value will lead to a huge decline in at least one other objective value.So this point is usually considered as a point that is more attractive to decision makers without special preferences.This article aims to summarize the methods related to Knee search in multi-objective optimization,including Knee detection methods and retention strategies,benchmark problems,etc.,and look forward to the future research work related to Knee search.