on the possibility to create a compatible--complete unary comparison method for evolutionary multiobjective algorithms
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.
performance measures pareto optimality multiobjective optimization