Space Trajectories Optimization

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We have tackled the space trajectory optimization problems proposed by the European Space Agency (ESA), which are reported in the Global Optimisation Trajectory Problems (GTOP) database.

Problem "TandEM-Atlas501" (MGA-1DSM - unconstrained continuous optimisation) and Solutions

Trajectories to Saturn: new optimal solutions found! Here is a list of the best solutions known for different fly-by sequences. Note that E = Earth, V = Venus, M = Mars, J = Jupiter, S = Saturn.

Tandem 21 (EEMVS)
f(x) = 812.216 (Best Result 12/10/2010)
Tandem 22 (EEMES)
f(x) = 1265.44 (Best Result 22/09/2010)
Tandem 23 (EEMMS)
f(x) = 1077.95 (Best Result 16/01/2010)
Fly-by-sequence: Earth - Earth - Mars - Mars - Saturn
x=[7150.99456094075139844790, 3.57480752856198513712, 0.99915424716023970575, 0.50004820950342421249, 1156.01480839114856280503, 1183.95038758726741434657, 2061.60917268165485438658, 2135.35176289286482642638, 0.73001148713891528264, 0.03214738068159579687, 0.03500600638026800382, 0.02767685627434375226, 1.05000002838412198614, 1.05000000025276429838, 1.05000000136370807979, -1.42981991083723025682, -1.47002800519075771390, -1.45484894103418715972]
Tandem 24 (EEMJS)
f(x) = 1209.26 (Best Result 10/06/2010)

Old Optimal Solutions:
Fly-by-sequence: Earth - Venus - Venus - Earth - Saturn (2)
f(x) = 1382.91 (best solution until 19/05/2010)
x=[8086.38545663006334507372, 3.54544514094441698404, 0.50023832331846662669, 0.53209674394570216638, 1177.33476369016216267482, 1837.93136548242409844534, 884.41257142907511479279, 2094.32125643636663880898, 0.83001514415292010352, 0.86798530023882813911, 0.41339061800772747279, 0.01045698143014894138, 1.60957913276256103785, 1.05000388948022904678, 1.07299614336371607060, -1.29221608686735001115, -1.25147621140407294682, -1.55912281084063852887]
Fly-by-sequence: Earth - Earth - Earth - Earth - Saturn (18)
f(x) = 1242.52 (best solution until 19/05/2010)
x=[7566.63541042059387109475, 2.51926541880680066043, 0.00027264342335383375, 0.50053832453337165909, 1405.78901672060123928532, 697.19039332925922280992, 1135.93416617048796979361, 1918.29699233894461940508, 0.86661302303990217499, 0.52860274725708866761, 0.48987174816305006919, 0.03163765830964872239, 1.76104221142023265045, 1.69099329782021179369, 1.05000000376733493290, -1.57075980440815277106, -1.57093144238065018925, -1.45987133412896730178]

The final mass is obtained from the objective function according to the expression: mass = (2 -objfun)*1000

Global Optimisation Trajectory Problems and Solutions

Problem "Messenger Full" (Note: difficult version)
f(x) = 6.404 km/s (best solution until 30/11/2009)
x= [1923.301277801785318, 4.049997370921471, 0.745404355252295, 0.492647705352134, 258.047114759643250, 111.551121330515471, 209.771097620485449, 263.910919680612551, 257.348169378748139, 358.726788262107107, 0.448924376131032, 0.104414240442925, 0.617419804607928, 0.550450701752095, 0.722250342844533, 0.821977409543496, 1.330394293289470, 1.100065724824133, 1.051071974831816, 1.050186622580361, 1.050124500186790, 0.437188374746588, 1.380966157972101, -0.176062635405350, -0.267307133687128, 1.563894388165100]
Problem "Messenger"
f(x)=8.630 km/s (ex-aequo result)
x=[1171.147864475932693,1.419852456607554,0.378051174875557,0.500049609313836,... 399.999998822765065,178.928109256163623,299.273690514292582,180.681646338738290,... 0.236452605602530,0.040137090962138,0.833009812857564,0.312663036125523,1.743829338338659,... 3.030420917033603,1.100000013578624,1.350925560861563,1.093486977487571,1.344932503494194]
Problem "Cassini 2"
f(x) = 8.383 kg km/s (ex-aequo result)
x=[-780.139650091233989, 3.274885038056841,0.530644278044670,0.382053046558889,168.479997362019617,... 423.996994280159015,53.306892653869760,589.771733121087664,2199.999844386815312,0.774478179540975,... 0.533231836184537,0.109296138673985,0.081656589179608,0.087814625231796,1.360972586934840,... 1.050000816262513,1.306796636144710,69.812361800511979,-1.594147053459453,-1.959565028967742,... -1.554773542899543,-1.513431345248221]
Problem "Rosetta"
f(x) = 1.343 km/s (ex-aequo result)
x=[1542.372459425032730,4.453448275481087,0.277057291383673,0.948772623472528,365.242384268506214,... 708.101973138050539,257.441421754157318,730.484326918843976,1849.999989744979757,0.426367810263889,... 0.809650912714183,0.021487307818609,0.139279647608137,0.435250522810427,1.050006345425601,... 1.050000005506522,2.637401495963678,1.208566046191566,-0.987319442592444,1.789494897734801,... -2.100825307607381,-1.871004346032785]
Problem "SAGAS"
f(x) = 18.19 years (ex-aequo result)
x=[7020.11,5.3453,0.0004,0.5003,789.4182,484.0004,0.4946,0.01,1.05,10.8522,-1.5720,-0.7003]

Reference

G. Stracquadanio, A. La Ferla, G. Nicosia, "SAGES: Self-Adaptive Gaussian Evolutionary Algorithm for Space Trajectories Optimization". Technical Report, CT-16022010, Department of Mathematics and Computer Science, University of Catania.

[Introduction] - [Contacts] - [Research] - [Publications] - [Projects] - [Events] - [Teaching] - [The Giants].

Giuseppe Nicosia, Optimization, Combinatorial Optimization, Numerical Optimization, Non Linear Optimization, Large Scale Optimization, Evolutionary Algorithms, Genetic Algorithms, Immune Algorithms, Artificial Immune Systems, Graph Coloring, String Folding, NP-complete problems, Circuit Optimization, Circuit Design, Design For Yield, Device Optimization, Bioinformatics, Structural Bioinformatics, Protein Folding, Protein Structure Prediction, HP model.