Global Optimization Approaches for Optimal Trajectory Planning

Optimal trajectory design for interplanetary space missions is an extremely hard problem, mostly because of the very large number of local minimizers that real problems present. Despite the challenges of the task, it is possible, in the preliminary phase, to design low-cost high-energy trajectories with little or no human supervision. In many cases, the discovered paths are as cheap, or even cheaper, as the ones found by experts through lengthy and difficult processes. More interestingly, many of the tricks that experts used to design the trajectories, like, e.g., traveling along an orbit in fractional resonance with a given planet, naturally emerge from the computed solutions, despite neither the model nor the solver have been explicitly designed in order to exploit such knowledge. In this chapter we will analyze the modelling techniques that computational experiments have shown to be most successful, along with some of the algorithms that might be used to solve such problems.