# GTOC 1

This instance of a Multiple Gravity Assist problem draws inspiration from the first edition of the Global Trajectory Optimisation Competition (GTOC1). It is an MGA problem with a rather long fly-by sequence including mainly Earth and Venus. The final target is the asteroid TW229. The objective of the mission is to maximise the change in sami-major axis of the asteroid orbit following an anaelastic impact of the spacecraft with the asteroid J(x) = m_f U v.

# The code

- MATLAB: use the function gtoc1.m and pass to it the MGAproblem variable contained in gtoc1.mat
- C++: call the function "double gtoc1(const std::vector & x, std::vector& rp)" provided in the GTOPtoolbox.
- C++ (PaGMO): use the class pagmo::problem::gtoc_1
- Python 2.7 (PyGMO): use PyGMO.problem.gtoc_1().obj_fun(x)

# Problem Description

The box bounds on each of the decision vector variable are given below.

## State | ## Variable | ## Lower Bounds | ## Upper Bounds | ## Units |
---|---|---|---|---|

State | Variable | LB | UB | Units |

x(1) | t0 | 3000 | 10000 | MJD2000 |

x(2) | T1 | 14 | 2000 | days |

x(3) | T2 | 14 | 2000 | days |

x(4) | T3 | 14 | 2000 | days |

x(5) | T4 | 14 | 2000 | days |

x(6) | T5 | 100 | 9000 | days |

x(7) | T6 | 366 | 9000 | days |

x(8) | T7 | 300 | 9000 | days |

Constraints on the various fly-by pericenters are also considered to the values:

- rp1 > 6351.8 km
- rp2 > 6778.1 km
- rp3 > 6351.8 km
- rp4 > 6778.1 km
- rp5 > 600000 km
- rp6 > 70000 km

Solutions are rounded to the fourth digit and only improvements on that level is considered. No constraint violation is allowed.

# Solutions:

The record holders of this problem are listed below in chronological order:

## Author | ## Affiliation | ## Date | ## Obj Fun | ## Solution | ## Algo |
---|---|---|---|---|---|

Tamas Vinko and Dario Izzo | European Space Agency | 23 Jan, 2008 | -1,580,599 | x=[6809.476683160, 169.598512787, 1079.375156244, 56.53776494142, 1044.014046276, 3824.160968179 1042.885114734 3393.057868710] | PaGMO |

M. Schlueter, M. Gerdts | University of Birmingham | Jan, 2010 | -1,581,950 | x=[6810.40521106, 168.37469758, 1079.47409963, 56.38731208, 1044.09288643, 3820.84181773, 1044.32726019, 3397.21349495] | MIDACO |