Problem "SAGAS" (MGA-1DSM)

This code evaluates the DV required to reach Jupiter using an Earth Earth Jupiter fly-by sequence with deep space manouvres.

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Short description

In this trajectory problem we design what is commonly called a deltaV-EGA manouvre to then fly-by Jupiter and reach 50AU. The objective function considered is the overall mission length and has to be minimsed. This creates an MGADSM problem where two more variables need to be added to the decision vector in order to be able to evaluate the keplerian orbit reached after the last fly-by. For the 12 dimension state vector we use the bounds given in following table:

As constraints we consider the deltaV capability of the spacecraft

deltaV_1 + deltaV_2 < 1.782,

and the total available

deltaV:=deltaV_1 + delta V_2 + delta V_infinity < 6.782 km/s.

Note that the bound on the departure deltaV is quite large and include a very strong minima at around 1-4 km/sec (1:1 Earth orbit resonance) that often tricks the optimisers. Clearly, by reducing this bound (knowledge-based pruning) one can drastically help any optimiser to locate the correct global optima. As here we are interested in the algorithmic performances, we selected the bounds to create an interesting optimisation problem rather than to simplify the problem as much as possible and thus we included zones of the search space one could prune out by experience.

The objective function is considered to the precision of 0.01 years.

Solutions

The best trajectory found so far (26 March, 2008), (credits: T., Vinko, D., Izzo using DiGMO):

J(x) = 18.19 years,

x=[7020.49, 5.34817, 1, 0.498915, 788.763, 484.349, 0.4873, 0.01, 1.05, 10.8516, -1.57191, -0.685429]