On the Hierarchical Structure of Pareto Critical Sets

In this talk we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the Pareto critical set is completely described by its boundary (eg_ if we have more objective functions than dimensions in the variable space), this can be used to solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set. This technique is especially useful for efficiently solving many -objective optimization problems by breaking them down into MOPs with a reduced number of objective functions. For further details on this topic, we refer to [1].