Expanding the Exploration of the Criterion Space for Multi-Objective Optimal Control Problems

A wide range of optimal control problems present multiple and conflicting objectives that need to be optimized at the same time. However, this multi-objective nature is most often neglected and typically it is tackled by constructing a global objective function consisting of a Weighted Sum (WS) of the single objectives. Unfortunately, this approach fails to present practitioners with a complete representation of the underlined trade-offs between the considered objectives. Multi-objective optimization proved to be a powerful tool to correctly describe these trade-offs in a set of optimal solutions known as the Pareto set. In this paper a new method to solve multi-objective optimal control problems based on geometric considerations is introduced. The method returns a wider Pareto set when compared to the methods available, hence improving the quality of the achieved solution. The proposed method is applied to the optimal control and design of a tubular reactor.