OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

"Non-invasive optimization of embedded large-scale and multi-scale systems" Eduardo Luna-Ortiz (School of Chemical Engineering and Analytical Science, The University of Manchester)

Abstract: A non-invasive optimization method which does not require the availability of the model equations (or its gradients) and that can be built around any transient simulator, treating it, as a closed black-box solver is presented. A reduced steady-state optimization framework is developed based on the the Recursive Projection Method (RPM), which combines the use of Picard iterations and Newton's method with an input/output simulator. It explodes the fact, that for many dissipative (PDE) systems, only a few modes of the eigenspectrum are necessary to represent the whole action of the system, an assumption that holds for many engineering systems. This will lead to the construction of only low-dimensional Jacobian and gradients that span the low-dimensional dominant eigenspectrum. A second reduction is performed by projecting the coupled system RPM/simulator onto the null subspace of the problem, since it is common that, in engineering, an optimization problem has very few degrees of freedom. The major computational gain comes from the fact that none of the high-dimensional Jacobians or Hessians ever needs be constructed or inverted. In the case of dynamic optimization, a multiple shooting discretization of the dynamic constraints is used. We combine a Newton-Picard-type Method, which identifies the low- dimensional slow dynamics of the (dissipative) model in each time subinterval of the multiple shooting discretization, with reduced Hessian techniques for a second reduction to the low-dimensional subspace of the control parameters. To demonstrate the capabilities of the optimization framework illustrative examples are provided using an in-house explicit time-stepping simulator and an embedded Computational Fluid Dynamics (CFD) model as black-box simulators.