Finding equidistant nondominated points for biobjective mixed integer programs

Martin Philip Kidd, Richard Martin Lusby, Jesper Larsen

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    The nondominated frontier of a multiobjective optimization problem can be overwhelming to a decision maker, as it is often either exponential or in nite 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 nding 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.
    Original languageEnglish
    Number of pages23
    Publication statusPublished - 2016


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