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.