Finding equidistant nondominated points for biobjective mixed integer programs

The nondominated frontier of a multiobjective optimization problem can be overwhelming to a decision maker, as it is often either exponential or infinite in size. Instead, a representation of this set in the form of a small sample of points is often preferred. In this paper we present a new biobjective criterion space search method for generating a small set of equidistant points based on the space division idea behind Voronoi diagrams. The motivation for this method stems from the finding that there exists a dual relationship between the well-established quality measures of coverage and uniformity, and that a set of equidistant points closes the gap. The method is easy to implement, and relies only on the availability of a black-box solver. We show on a benchmark set of biobjective mixed integer programming instances that the method outperforms the state of the art with respect to both coverage and uniformity.