Algorithms and Software for Simulation Based Optimization
Most of real world applications can be formulated in mathematical terms. Many of the applications have a specific structure which can be exploited in most of the cases and allow for an efficient numerical simulation. These structural characteristics should be taken care of in the context of mathematical optimization, where one wants to minimize/maximize a certain objective functional based upon the simulation. In particular, instead of considering general-purpose NLP solvers we pursue the idea to develop optimization algorithms for some classes of problems that exploit the underlying structure but are still as general as possible.
A focus in this talk will be an ongoing project concerning geothermal simulation and one-shot optimization. Here, the underlying simulation is based on underground flows in porous media that can be controlled by the positioning of the inlets and outlets for the fluid. Therefore, a two-phase flow is solved using a splitting method that solves the pressure equation and the saturation equation in an alternating fashion. The resulting numerical simulation code can be regarded as a slowly converging fixed point iteration for the physical quantities such as pressure and saturation. Hence, we consider a one-shot optimization strategy for achieving the point-wise maximal temperature at one outlet that is computed by solving the heat equation for stationary phase saturations and fluid velocities.