This paper presents an incremental approach to the solution of multiple gravity assist trajectories (MGA) with deep space maneuvers. The whole problem is decomposed in sub-problems that are solved incrementally. The solution of each sub-problem leads to a progressive reduction of the search space. Unlike other similar methods, the search for solutions of each sub-problem is performed through a stochastic approach. The resulting set of disconnected boxes is transformed into a connected collection of boxes through an affine transformation. For MGA problems, the incremental approach increases both the efficiency and reliability of the optimization process. Two relevant examples will illustrate the effectiveness of the proposed method
