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.

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective optimization problems. This paper presents two methods for generating discrete representations with equidistant points for biobjective problems with solution sets determined by convex, polyhedral cones. The Constraint Controlled-Spacing method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. The Bilevel Controlled-Spacing method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing, and is extended to multiobjective problems. Both methods are proven to produce (weakly) nondominated points and are demonstrated on a variety of test problems.