Informatics
GTOP Database: Global Optimisation Trajectory Problems and Solutions
 Problem "TandEM-Atlas501" (MGA-1DSM) TandEM is an interplanetary trajectory with multiple fly-bys. The transcription proposed here uses one deep-space manouvre per leg, and a launch with the rocket Atlas 501, the performances being taken here.
 Download MATLAB: use the function tandem.m and pass to it the MGADSMproblem variable contained in tandem.mat after having selected the correct sequence in MGADSMproblem.sequence C++: call the function double tandem(const std::vector & x, double& tof, const int sequence_[]) function provided in the GTOPtoolbox.
 Short description The global optimisation problems we propose draw inspiration from the work performed in April 2008 by the European Space Agency working group on mission analysis on the mission named TandEM. TandEM is an interplanetary mission aimed at reaching Titan and Enceladus (two moons of Saturn). The problems, written here as minimisation problems, are actually maximising the mass delivered to a high eccentricity final orbit. With respect to the other mgadsm problems proposed in these pages, the transcription of the TandEM problem is slightly different as it evaluates directly the spacecraft mass at departure, and then at the end, using an interpolation of the launcher capability table (declination and C3 vs mass). The fly-by sequence can be selected among the ones suggested later. Each fly-by sequence creates a different problem instance. The wide bounds given below can be used for all problem instances.
 The problems We propose two sets of 25 different instances: Unconstrained continuous optimisation (best solutions known) Constrained continuous optimisation (best solutions known) : A constraint on the total mission duration is considered: x(5)+x(6)+x(7)+x(8) < 3652.5. [In the C++ code c_ineq (output of the tandem function) needs to be negative]
 Credits: Credits for the transcription of the TandEM problem and the creation and mainteinance of these web pages go to Dario Izzo and Marco del Rey Zapatero.

Bounds: The bounds below are valid for all problem instances. The fly-by altitude bounds x(13)-x(15) are not realistic when the planet Jupiter is included in the sequence. As the purpose of this web-page is purely academic, we decided not to complicate the problem description further by having bounds depending on the problem instance.

 State Variable LB UB Units x(1) t0 5475 9132 MJD2000 x(2) Vinf 2.5 4.9 km/sec x(3) u 0 1 n/a x(4) v 0 1 n/a x(5) T1 20 2500 days x(6) T2 20 2500 days x(7) T3 20 2500 days x(8) T4 20 2500 days x(9) eta1 0.01 0.99 days x(10) eta3 0.01 0.99 n/a x(11) eta3 0.01 0.99 n/a x(12) eta4 0.01 0.99 n/a x(13) r_p1 1.05 10 n/a x(14) r_p2 1.05 10 n/a x(15) r_p3 1.05 10 n/a x(16) b_incl1 -pi pi n/a x(17) b_incl2 -pi pi n/a x(18) b_incl3 -pi pi n/a
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