Problem "Messenger" (MGA-1DSM)

This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem.

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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:

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

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)

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)

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]