Towards a link between knee solutions and preferred solution methdologies

Abstract

In a bi-criteria optimization problem, often the user is interested in a subset of solutions lying in the knee region. On the other hand in many problem-solving tasks, often one or a few methodologies are commonly used. In this paper, we argue that there is a link between the knee solutions in bi-criteria problems and the preferred methodologies when viewed from a conflicting bi-criterion standpoint. We illustrate our argument with the help of a number of popularly used problem-solving tasks. Each task, when perceived as a bicriteria problem, seems to exhibit a knee or a knee-region and the commonly-used methodology seems to lie within the knee-region. This linking is certainly an interesting finding and may have a long-term implication in the development of efficient solution methodologies for different scientific and other problem-solving tasks.