On the quality of discrete representations in multiple objective programming

Within the past ten years, emphasis has been placed on generating discrete representations of the nondominated set which are truly representative of the nondominated set as a whole. This paper reviews measures for assessing the quality of discrete representations as well as exact solution methods that attempt to produce representations satisfying certain quality criteria. The measures are classified according to the aspect of the representation which they assess: cardinality, coverage, or spacing. The proposed solution methods are categorized according to whether a measure is integrated into the procedure a priori (before generation of solution points), a posteriori (after the generation of solution points), or not at all. The paper concludes with a comparative discussion of these three approaches and directions for future research.