The aim of this project is to transfer error estimation and mesh refinement techniques established in PDE simulation and optimization to discrete optimization problems involving continuous components in space, time, and state. The vision is to use such relaxations for the efficient computation of lower bounds on the dual side, and for the fast construction of feasible solutions on the primal side. The ultimate goal is a general method that gives a priori and a posteriori control of the trade-off between speed and accuracy, in solvers that are faster and more precise than today.
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The project develops an adaptive mesh refinement method based on a continuous PDE relaxation that can be used as a plug-in in branch&bound solvers as the CIP optimizer SCIP as well as in special purpose methods such as the railway rotation optimizers TS-OPT and ROTOR, and the aircraft trajectory optimizer VOLAR. Aircraft trajectory optimization will be the initial test case, and VOLAR the development platform and demonstrator.
The aim is to transfer error estimation and mesh refinement techniques established in PDE simulation and optimization to discrete optimization problems involving continuous components in space, time, and state. The vision is to use such relaxations for the efficient computation of lower bounds on the dual side, and for the fast construction of feasible solutions on the primal side. The ultimate goal is a general method that gives a priori and a posteriori control of the trade-off between speed and accuracy, in solvers that are faster and more precise than today.