• ## Global Trajectory Optimisation Problems Database

Laurelin, the trajectory that ranked second in the sixth edition of the GTOC competition, has been obtained as a solution to a complex global optimization problem.

The GTOP web pages contain the definition of black-box global optimisation spacecraft trajectory problems and their best putative solutions. Should you find a better solution to one or more of these problems, please submit it via e-mail to:

## The code

We are making available several difficult trajectory optimisation problems as black box functions to invite the operational research community, the evolutionary computations community and the aerospace engineers to develop, apply and compare different derivative-free solvers on these test problems. The code is made available in C++, MATLAB and Python, but it is no longer maintained.

1. For MATLAB download the two core functions mga.m and mga_dsm.m and then use the different function wraps given in each one of the problem page.
2. For C++ download the GTOPtoolbox (LAST VERSION: 12/10/2012) containing all the necessary functions and examples. As an alternative (preferred method) you may download PaGMO (the version 1.x) and you will find there, in the namespace pagmo::problems, all GTOP database problems (check the doxygen).
3. For Python 2.7 you can install PyGMO (the verison 1.x) and find all problems in the PyGMO.problem module

## MGA Global Optimisation Problems

A simple benchmark to test global optimisation algorithms in Space Mission Design related problems is the Multiple Gravity Assist (MGA) problem. In mathematical terms this is a finite dimension global optimisation problem with non linear constraints. It can be used to locate the best possible trajectory that an interplanetary probe equipped with a chemical propulsion engine may take to go from the Earth to another planet or asteroid. The spacecraft is constrained to thrust only at planetary encounters.

Problem list

## MGA-1DSM Global Optimisation Problems

The constraint on the spacecraft thrusting only only at planetary encounters is often unacceptable as it may results in trajectories that are not realistic or that use more propellant than necessary. The MGA-1DSM problem removes most of these limitations. It represents an interplanetary trajectory of a spacecraft equipped with chemical propulsion, able to thrust its engine once at any time during each trajectory leg. Thus the solutions to this problem are suitable to perform preliminary quantitative calculation for real space missions. This comes to the price of having to solve an optimisation problem of larger dimensions.

Problem list

## Solvers tested

The following algoritmic paradigms have been tested on some of the problems in this database: Differential Evolution, Particle Swarm Optimisation, Genetic Algorithm, Simulated Annealing, Self-Adaptation, the Island Model, Improved Harmony Search, Artificial Bee Colony, Monotonic Basin Hopping, Covariance Matrix Adaptation Evolutionary Strategy. All the code associated to these solvers is made available as part of the open source project PaGMO/PyGMO V1.x

## Outcome

1. Izzo, D. 2010. “Global Optimization and Space Pruning for Spacecraft Trajectory Design.” In Spacecraft Trajectory Optimization, edited by B. Conway, 178–99 Cambridge University Press. [link]

2. Vinko, T., D. Izzo, and C. Bombardelli. 2007. “Benchmarking Different Global Optimisation Techniques for Preliminary Spacetrajectory Design.” In Paper IAC-07-A1.3.01, 58th International Astronautical Congress, Hyderabad, India. [link]

3. Vinko, T., and D. Izzo. 2008. “Global Optimisation Heuristics and Test Problems for Preliminary Spacecraft Trajectory Design.” GOHTPPSTD European Space Agency, the Advanced Concepts Team. [link]