Study of Genetic Algorithm Settings for Trajectory Optimisation

Abstract

Genetic algorithms have been used for over 20 years in various applications of optimisation. Also, in optimisation of space applications these algorithms have been studied and occasionally used. Applications of genetic algorithms in the European Space Agency (ESA) date back to 1985. Both advantages (fast convergence for problems with many parameters, no need for derivatives and initial guess) and disadvantages (often no full convergence to global optimum, difficulties implementing constraints) are now well known. The genetic algorithm (GA) parameters such as cross-over probability, mutation probability, population size play an important role on the convergence. Although some standard settings were published before, usually for each unique problem a unique set of GA parameters exists. In this paper the results of a study of these parameters, when applied to trajectory optimisation, are shown. Three cases are tested to evaluate these genetic algorithm settings. It can be seen that for the cases shown, the population size is the largest tuning factor whereas other parameters of cross-over and mutation probability have a smaller effect. For cases with convergence difficulties, the influence of the random generator can be reduced by re-starting the GA with a small number of generations instead of one run with a large number of generations.