The optimal design of multi-target rendezvous and flyby missions is challenging due to the combination of traditional spacecraft trajectory optimization and high-dimensional combinatorial problems. The typical approach to these problems generally requires large-scale global search techniques or simplified approximations relying on large amounts of manual labour to be performant. However, global search techniques are generally difficult to use in time- or cost-constrained scenarios due to their computational expense. This work proposes a novel combination of computationally efficient stages which work together to form a nested global optimization approach for multi-target mission design. The multi-target problem is split into seperate combinatorial and optimal control subproblems, which are recursively solved: the combinatorial problem using a novel Binary Integer Programming (BIP) formulation with fixed rendezvous timings obtaining optimal rendezvous ordering, and the optimal control problem with an adaptive-mesh Sequential Convex Programming (SCP) formulation obtaining optimal rendezvous timings for a fixed rendezvous ordering. These stages work recursively in tandem to improve the inputs to each subsequent stage until convergence is obtained. This methodology is demonstrated to offer state-of-the-art performance when applied to the Global Trajectory Optimization Competition 12 (GTOC 12) problem, to which several new best-known solutions are found.

We present the solution approach developed by the team "TheAntipodes" during the 12th edition of the Global Trajectory Optimization Competition (GTOC12). An overview of the approach is as follows: (1) generate asteroid subsets, (2) chain building with beam search, (3) convex low-thrust trajectory optimization, (4) manual refinement of rendezvous times, and (5) optimal solution set selection. The generation of asteroid subsets involves a heuristic process to find sets of asteroids that are likely to permit high-scoring asteroid chains. Asteroid sequences "chains" are built within each subset through a beam search based on Lambert transfers. Low-thrust trajectory optimization involves the use of sequential convex programming (SCP), where a specialized formulation finds the mass-optimal control for each ship's trajectory within seconds. Once a feasible trajectory has been found, the rendezvous times are manually refined with the aid of the control profile from the optimal solution. Each ship's individual solution is then placed into a pool where the feasible set that maximizes the final score is extracted using a genetic algorithm. Our final submitted solution placed fifth with a score of 15,489.