Solving Multi-Objective Optimal Control Problems Using a Multiresolution Approach

This paper presents an adaptive multiresolution strategy for multi-objective optimal control problems. The optimal control problem is solved using a direct approach, with individualistic grid adaptation facilitated by a local error analysis at element boundaries. Multiple objectives are considered using a dominance-based approach applying both local and global search methods to a collaborative population of unique solutions. These aspects are simultaneously incorporated via a novel application of evolutionary algorithms for adaptive optimal control problems. Together, this avoids the need for a priori specification of the quantity and temporal location of element boundaries and the set of scalarization weights defining the multi-objective descent directions. Solution fidelity can thus increase concurrently with the exploration of the design space, which leads to increased numerical efficiency while propagating and maintaining population diversity. The benefits of the proposed approach over traditional uniform-grid implementations are demonstrated. Results show that the multiresolution approach is capable of striking an effective balance between solution fidelity, population diversity, and computational cost unachievable using uniform grids.