With the current setup, the optimization links like a chain: we optimize one spacecraft at a time, passing the updated tensor between them and thus reducing the search space for all upcoming optimization processes. In other words, we can view the complete process as indirectly maximizing the total coverage by minimizing overlapping trajectories for each spacecraft at a time. By doing so, it is evident that the solution will converge at some optima for the specific configuration, which is likely to be a local optima for the complete problem.
However, this dependency could potentially be avoided by introducing a master problem. The subproblem could, for instance, be to determine a set of optimized single spacecraft trajectories, where the master problem then finds the optimal combination w.r.t total coverage. What do you think? This may be unnecessary since the current setup will likely provide something good, just not optimal. I was perhaps just worried about the chain-like dependencies in the current structure.
With the current setup, the optimization links like a chain: we optimize one spacecraft at a time, passing the updated tensor between them and thus reducing the search space for all upcoming optimization processes. In other words, we can view the complete process as indirectly maximizing the total coverage by minimizing overlapping trajectories for each spacecraft at a time. By doing so, it is evident that the solution will converge at some optima for the specific configuration, which is likely to be a local optima for the complete problem.
However, this dependency could potentially be avoided by introducing a master problem. The subproblem could, for instance, be to determine a set of optimized single spacecraft trajectories, where the master problem then finds the optimal combination w.r.t total coverage. What do you think? This may be unnecessary since the current setup will likely provide something good, just not optimal. I was perhaps just worried about the chain-like dependencies in the current structure.