joint work with Nicolò Robuschi, Sebastian Sager, Francesco Braghin
This talk considers the problem of computing the minimum-fuel energy management strategy of a hybrid electric vehicle on a given driving cycle. A tailored algorithm is devised by extending the combinatorial integral approximation technique that breaks down the original mixed-integer nonlinear program into a sequence of nonlinear programs and mixed-integer linear programs. Specifically, we address the multiphase context and propose combinatorial constraints for the optimal gear choice, torque split and engine on/off controls in order to account for technical requirements.
We present algorithms to solve mixed integer problems constrained by partial differential equations (PDEs). A branch and bound methodology is used to address the discrete nature of the problem and at each bound computation the relaxation requires the solution of a PDE-constrained optimization problem. A hierarchical modeling approach (with multiple starts) efficiently supports the bounding process. Low-fidelity models allow exploration for the most promising branching options. We discuss our C++ software design which features scalable parallelism. A numerical prototype demonstrates our approach.
joint work with Ryan Vogt, Todd Munson
We formulate a mixed-integer partial-differential equation constrained optimization problems (MIPDECO) for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and develop a mixed-integer trust-region approach for solving both the nominal and the uncertain instance. Our method alternates between a forward/adjoint PDE solve and a knapsack problem. We present numerical results of our new approach that demonstrate its effectiveness.