On the possibility to create a compatible--complete unary comparison method for evolutionary multiobjective algorithms

Abstract

There are several studies on the desirable properties that a performance measure for evolutionary multiobjective algorithms must have. One of these properties is called "compatibility and completeness". There is a theorem that proves that in the general case, it is not possible to create a unary comparison method with the property mentioned before. Many important conclusions have been derived from this theorem, so its correctness is fundamental for future research. In this work we demonstrate that under practical conditions, the theorem mentioned before does not hold.

Quality Evaluation of Solution Sets in Multiobjective Optimisation

“…Theoretical studies of QIs. This category works on some important issues in the design of QIs, including analyses of the computational complexity of QIs Bringmann and Friedrich (2012); Fonseca et al (2006); While et al (2012), and discussions of some properties that a QI (or a combination of QIs) desires for, such as Pareto compatibility and completeness Knowles et al (2006); Lizárraga-Lizárraga et al (2008b); Zitzler et al (2003), scaling invariance Zitzler et al (2008), and minimum set construction Farhang-Mehr and Azarm (2003b).…”