On cone based decompositions of proper Pareto optimality

In recent years, the research focus in multi-objective optimization has shifted from approximating the Pareto optimal front in its entirety to identifying solutions that are well-balanced among their objectives. Proper Pareto optimality is an established concept for eliminating Pareto optimal solutions that exhibit unbounded tradeo ffs. Imposing a strict tradeo ff bound allows specifying how many units of one objective one is willing to trade in for obtaining one unit of another objective. This notion can be translated to a dominance relation, which we denote by M-domination. The mathematical properties of M-domination are thoroughly analyzed in this paper yielding key insights into its applicability as decision making aid. We complement our work by providing four diff erent geometrical descriptions of the M-dominated space given by a union of polyhedral cones. A geometrical description does not only yield a greater understanding of the underlying tradeoff concept, but also allows a quanti cation of the space dominated by a particular solution or an entire set of solutions. These insights enable us to formulate volume-based approaches for finding approximations of the Pareto front that emphasize regions that are well-balanced among their tradeoff s in subsequent works.



View On cone based decompositions of proper Pareto optimality