We present a new two-step approach for automatized a posteriori decision making in
multi-objective optimization problems, i.e., selecting a solution from the Pareto front. In the first step,
a knee region is determined based on the normalized Euclidean distance from a hyperplane defined
by the furthest Pareto solution and the negative unit vector. The size of the knee region depends on
the Pareto front’s shape and a design parameter. In the second step, preferences for all objectives
formulated by the decision maker, e.g., 50–20–30 for a 3D problem, are translated into a hyperplane
which is then used to choose a final solution from the knee region. This way, the decision maker’s
preference can be incorporated, while its influence depends on the Pareto front’s shape and a design
parameter, at the same time favorizing knee points if they exist. The proposed approach is applied in
simulation for the multi-objective model predictive control (MPC) of the two-dimensional rocket car
example and the energy management system of a building
