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The aim of this article is to analyse the results obtained when using a genetic algorithm (GA) to optimise the interplanetary trajectory of a spacecraft. The desired trajectory should visit Saturn, after performing a gravitational assistance or fly-by in planet Mars. The GA tunes a set of variables, in order to achieve the mission purpose while satisfying the constraints and minimizing the delta-V of the mission. Due to the complexity of the implemented models and the lack of analytical solutions, an alternative non-traditional algorithm provided by soft-computing techniques such as GA is necessary to achieve an optimum solution. The positions of planets as provided by Jet Propulsion Laboratory have been considered. A variable mutation rate has been implemented that broadens the search area whenever the population becomes uniform. The results are very useful from the point of view of mission analysis and therefore can be used as an initial guess for further optimizations. They can also be the first step for a more refined analysis and time-consuming simulations based on more complex models of orbital perturbations.