I'll tell you what I want: Categorization of Pareto Fronts for Automated Rule-based Decision-Making

Abstract

The application of Pareto optimization in control engineering requires decision-making as a downstream step since one solution has to be selected from the set of computed Pareto optimal points. Economic Model Predictive Control (MPC) requires repeated optimization and, in multi-objective optimization problems, selection of Pareto optimal points at every time step. Thus, designing an automated selection strategy is favorable. However, it is challenging to come up with a measure – possibly based on a Pareto front analysis – that characterizes preferred Pareto optimal points uniformly across different Pareto fronts. In this work, we first discuss these difficulties for application within MPC and then suggest a solution based on unsupervised machine learning methods. The approach is based on categorizing Pareto fronts as an intermediate step. This allows generating an individual set of rules for every category. Thereby, the human decision-maker's preferences can be modeled more accurately and the selection of a Pareto optimal solution becomes less time-consuming while breaking down the decision-making process into a selection solely based on the Pareto front's shape. Here, the measures act as anchor points for the decision rules. Lastly, a novel knee point measure, i.e. an approximation of the Pareto front's curvature, is presented and used for a knee point-focused categorization. The proposed algorithm is successfully applied to a case study for an energy management system. Moreover, we compare our method to using singular measures for decision-making in order to show its higher flexibility leading to better performance of the controller.