Optimization problems in Space Geodesy

In all the computations carried out in Space Geodesy, we are confronted with optimization problems. These latter can roughly be classified in two main categories. (i) Combinatorial problems: subset problems (search of an instrument sub-network optimizing a given criterion or of an optimal co-location site sub-network), classification problems (division of a global dense GNSS antenna network into several well distributed sub-networks to optimize the computation time), etc. (ii) General problems (with or without constraints): search for the optimal position, on the Earth's surface, of a new observation instrument, design of adaptive basis functions, such as wavelets, to represent the Earth's gravity field with high resolution, computation of satellites orbits, etc. The large amount of data that requires to be processed, together with the possible ill-posed nature of some problems, do not allow us applying classical and/or deterministic approaches. We thus aim to solve all these problems on the basis of stochastic algorithms (possibly hybridized with deterministic methods), such as genetic algorithms. This paper first aims at briefly describing some of the problems summarily listed above. Then, the design of the algorithm applied and the results obtained are explained for some particular combinatorial and general problems.