A study of multi-objective optimization: focus on Knee

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. © 2021, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.