  Multi-rendezvous spacecraft trajectory optimization problems are notoriously
difficult to solve. For this reason, the design space is usually pruned by
using heuristics and past experience. As an alternative, the current research
explores some properties of $\Delta V$ matrices which provide the minimum
$\Delta V$ values for a transfer between two celestial bodies for various times
of departure and transfer duration values. These can assist in solving
multi-rendezvous problems in an automated way. The paper focuses on the problem
of, given a set of candidate objects, how to find the sequence of $N$ objects
to rendezvous with that minimizes the total $\Delta V$ required. Transfers are
considered as single algebraic objects corresponding to $\Delta V$ matrices,
which allow intuitive concatenation via a generalized summation. Waiting times,
both due to mission requirements and prospects for cheaper and faster future
transfers, are also incorporated in the $\Delta V$ matrices. A transcription of
the problem as a shortest path search on a graph can utilize a range of
available efficient shortest path solvers. Given an efficient $\Delta V$ matrix
estimator, the new paradigm proposed here is believed to offer an alternative
to the pruning techniques currently used.
