Informatics
GTOP Database: Global Optimisation Trajectory Problems and Solutions
 Problem "Messenger" (MGA-1DSM) This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem.
 Download MATLAB: use the function messenger.m and pass to it the MGADSMproblem variable contained in messenger.mat C++: call the function double messenger(const std::vector& x) function provided in the GTOPtoolbox.

Short description

This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem. The selected fly-by sequence is the same used in the first part of the Messenger mission. It is well known that a significant reduction of the required deltaV is possible if a number of resonant fly-bys follow the first Mercury encounter. Here we did not include that part of the trajectory in the optimisation problem as the dynamical model needed to represent multiple revolution solutions was not present in the code we planned to put on-line. We plan to publish the full trajectory problem description in a future work. For the eighteen dimensional global optimisation problem we consider the bounds listed in the following table:

 State Variable LB UB Units x(1) t0 1000 4000 MJD2000 x(2) Vinf 1 5 km/sec x(3) u 0 1 n/a x(4) v 0 1 n/a x(5) T1 200 400 days x(6) T2 30 400 days x(7) T3 30 400 days x(8) T4 30 400 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 1.1 6 n/a x(14) r_p2 1.1 6 n/a x(15) r_p3 1.1 6 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

No other constraints are considered for this problem. The objective function is considered to the precision of meters per second.

 Solutions A first trajectory has been found (26 March, 2008), (credits: T., Vinko, D., Izzo using DiGMO): J(x) = 8.703 km/s, x=[2369.89, 1.67208, 0.380256, 0.499911, 400, 168.06, 224.695, 212.292, 0.237501, 0.0223169, 0.161132, 0.468419, 1.80818, 1.64195, 1.1, 1.29702, 2.80363, 1.57266]. A better solution has been found (29 May, 2008) credits: B. Addis, A. Cassioli, M. Locatelli, F. Schoen (Global Optimization Laboratory, University of Florence J(x) = 8.643 km/s, x=[1172.41245754, 1.39439442686, 0.386119780527, 0.486013191263, 399.9997801, 178.058539963, 298.851878201, 180.302047179, 0.227024902551, 0.042965801672, 0.798285909365, 0.320498598568, 1.82076285084, 3.04644407208, 1.1, 1.34783991234, 1.09665911253, 1.34433291701] A better solution has been found (29 May, 2008) credits: B. Addis, A. Cassioli, M. Locatelli, F. Schoen (Global Optimization Laboratory, University of Florence) J(x) = 8.631 km/s, x=[1171.64503236 1.40899421278 0.37992647165 0.498004040298 399.999999715 178.372255301 299.223139512 180.510754824 0.234594654679 0.0964769387134 0.829948744508 0.317174785637 1.80629232251 3.04129845698 1.10000000891 1.35077257078 1.09554368115 1.34317576594] The best solution found so far (10 Feb, 2009) credits: F. Biscani, M. Rucinski and D.Izzo (using PaGMO, a new version of DiGMO based on the asynchronous island model) J(x) = 8.630 km/s, x=[1171.64503236, 1.40899421278, 0.37992647165, 0.498004040298, 399.999999715, 178.372255301, 299.223139512, 180.510754824, 0.234594654679, 0.0964769387134, 0.829948744508, 0.317174785637, 1.80629232251, 3.04129845698, 1.10000000891, 1.35077257078, 1.09554368115, 1.34317576594]
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