Understanding knee points in bicriteria problems and their implications as preferred solution principles |
| |
Authors: | Kalyanmoy Deb Shivam Gupta |
| |
Affiliation: | 1. Kanpur Genetic Algorithms Laboratory, Department of Mechanical Engineering , IIT Kanpur , 208016, India;2. Department of Business Technology , School of Economics, Aalto University , P.O. Box 21210, FI-00076, Aalto, Finland deb@iitk.ac.in;4. Department of Civil Engineering , IIT Kanpur , 208016, India |
| |
Abstract: | 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. |
| |
Keywords: | knee point preferred solutions bicriteria problems evolutionary algorithms NSGA-II |
|
|