GTOPX - Space Mission Benchmarks


Here you can download some real-world interplanetary space mission trajectory design benchmark problems. The GTOPX library is an extension of the well-known but no longer maintained GTOP database published in 2005 by ESA (European Space Agency). GTOPX consists of ten benchmark instances, whereas the last three (Cassini1-MINLP, Cassini1-MO and Cassini1-MO-MINLP) are newly introduced, featuring mixed-integer and multi-objective properties. All problem objective functions are to be minimized, all constraints are feasible if greater or equal to zero. Lower and upper bounds for the search space of each problem are defined in the below main file. Note that the GTOPX problems are generally considered to be  difficult  to solve, with possible exception of the Cassini1 and Sagas instances, which are rather easy to medium. Therefore researchers should not be discouraged if struggling to solve these benchmarks. Instead, the GTOPX library aims at senior researchers wishing to put advanced algorithms to the test. A paper describing the benchmarks is available here.


 GTOPX Benchmarks

No. Benchmark Name Ref Objectives Variables Constraints Solution  f(x)



1 Cassini1 NASA 1 6  4 4.9307
2 Cassini2 Wiki 1  22  0 8.3830
3 Messenger (reduced) NASA 1  18  0 8.6299
4 Messenger (full) Wiki 1  26  0 1.9579
5 GTOC1 Turin 1  8  6 -1581950.0
6 Rosetta ESA 1  22  0  1.3433
7 Sagas ESA 1  12  2  18.1877
8 Cassini1-MINLP Paper 1  10  4 3.5007
9 Cassini1-MO Paper 2  6  5



10 Cassini1-MO-MINLP Paper 2  10  5




GTOPX source code / library

C main.c gtopx.cpp makefile
C++ main.cpp






gtopx.dll   ( Windows 32bit )

gtopx.dll   ( Windows 64bit )   ( Linux 32bit )   ( Linux 64bit )   ( Mac 32bit )   ( Mac 64bit )






GTOPX is published under a GPL license



Usage Instruction




Step 1 Download main and gtopx source code file
Step 2 Compile and execute (e.g. using the makefile)

The gtopx.cpp file differs for C and C++ usage, as for C usage

the gtopx.cpp includes an  extern "C"  statement in Line 555




Step 1 Download main file together with gtopx library file
Step 2 Remove ".txt" name extension from file
Step 3 Execute by entering command "python"

Linux and Mac users might need to have g++ installed

to match dependencies of the library




Step 1 Download main file together with gtopxmex.cpp file
Step 2 Open Matlab and set the  Current Directory  to the above files
Step 3

Execute  "mex gtopxmex.cpp"  in the Command Window,

this command will create a mex library file on your system.

Step 4 Run the main program (e.g. type "main" and press Enter)
Note The mex command needs to be performed only once.


MIDACO Record Solutions

MIDACO holds the best known record solutions on the Cassini2, GTOC1 and Messenger (full) benchmarks. Note that the Messenger (full) benchmark is considered the most difficult instance and it's putative global solution required well  over 5 years  to be reached (see paper for details).



Author(s) Title Journal / Reference


Schlueter M. Mehdi N., Mohamed W., Masaharu M., Wagner M. GTOPX Space Mission Benchmarks

SoftwareX (Elsevier), Volume 14 (2021)


Schlueter M. MIDACO Software Performance on Interplanetary Trajectory Benchmarks Advances in Space Research (Elsevier), Vol 54, Issue 4, Pages 744 - 754 (2014)


Schlueter M., Munetomo M. A Mixed-Integer Extension for ESA's Cassini1 Space Mission Benchmark

Proceedings of the IEEE Congress on Evolutionary Computation (CEC2019), Wellington, New Zealand, Jun 10-13, DOI: 10.1109/CEC.2019.8790045 (2019)

Schlueter M., Wahib M., Munetomo M. New state-of-the-art results on ESA’s Messenger Space Mission Benchmark
Advances in Parallel & Distributed Processing, and Applications, Pages 669-681 (Springer) 2021 Preprint


See  here  for more publications.