  This paper addresses the problem of planning successive Space Debris
Collecting missions so that they can be achieved at minimal cost by a generic
vehicle. The problem mixes combinatorial optimization to select and order the
debris among a list of candidates, and continuous optimization to fix the
rendezvous dates and to define the minimum fuel orbital maneuvers. The solution
method proposed consists in three stages. Firstly the orbital transfer problem
is simplified by considering a generic transfer strategy suited either to a
high thrust or a low thrust vehicle. A response surface modelling is built by
solving the reduced problem for all pairs of debris and for discretized dates,
and storing the results in cost matrices. Secondly a simulated annealing
algorithm is applied to find the optimal mission planning. The cost function is
assessed by interpolation on the response surface based on the cost matrices.
This allows the convergence of the simulated algorithm in a limited computation
time, yielding an optimal mission planning. Thirdly the successive missions are
re-optimized in terms of transfer maneuvers and dates without changing the
debris order. These continuous control problems yield a refined solution with
the performance requirement for designing the future Space Debris Collecting
vehicle. The method is applicable for large list of debris and for various
assumptions regarding the cleaning program (number of missions, number of
debris per mission, total duration, deorbitation scenario, high or low thrust
vehicle). It is exemplified on an application case with 3 missions to plan,
each mission visiting 5 SSO debris to be selected in a list of 21 candidates.
