期刊
ENGINEERING OPTIMIZATION
卷 43, 期 11, 页码 1175-1204出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/0305215X.2010.548863
关键词
knee point; preferred solutions; bicriteria problems; evolutionary algorithms; NSGA-II
资金
- Department of Science and Technology, Government of India, under the SERC [SR/S3/MERC/091/2009]
A knee point is almost always a preferred trade-off solution, if it exists in a bicriteria optimization problem. In this article, an attempt is made to improve understanding of a knee point and investigate the properties of a bicriteria problem that may exhibit a knee on its Pareto-optimal front. Past studies are reviewed and a couple of new definitions are suggested. Additionally, a knee region is defined for problems in which, instead of one, a set of knee-like solutions exists. Edge-knee solutions, which behave like knee solutions but lie near one of the extremes on the Pareto-optimal front, are also introduced. It is interesting that in many problem-solving tasks, despite the existence of a number of solution methodologies, only one or a few of them are commonly used. Here, it is argued that often such common solution principles are knee solutions to a bicriteria problem formed with two conflicting goals of the underlying problem-solving task. The argument is illustrated on a number of tasks, such as regression, sorting, clustering and a number of engineering designs.
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