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It is a very challenging task to identify the objectives on which a certaindecision was based, in particular if several, potentially conflicting criteriaare equally important and a continuous set of optimal compromise decisionsexists. This task can be understood as the inverse problem of multiobjectiveoptimization, where the goal is to find the objective vector of a given Paretoset. To this end, we present a method to construct the objective vector of amultiobjective optimization problem (MOP) such that the Pareto critical setcontains a given set of data points or decision vectors. The key idea is toconsider the objective vector in the multiobjective KKT conditions as variableand then search for the objectives that minimize the Euclidean norm of theresulting system of equations. By expressing the objectives in afinite-dimensional basis, we transform this problem into a homogeneous, linearsystem of equations that can be solved efficiently. There are many importantpotential applications of this approach. Besides the identification ofobjectives (both from clean and noisy data), the method can be used for theconstruction of surrogate models for expensive MOPs, which yields significantspeed-ups. Both applications are illustrated using several examples.

Inverse multiobjective optimization: Inferring decision criteria from data