  In several important routing contexts it is required to identify a set of
routes, each of which optimizes a different criterion. For instance, in the
context of vehicle routing, one route would minimize the total distance
traveled, while other routes would also consider the total travel time or the
total incurred cost, or combinations thereof. In general, providing such a set
of diverse routes is obtained by finding optimal routes with respect to
different sets of weights on the network edges. This can be simply achieved by
consecutively executing a standard shortest path algorithm. However, in the
case of a large number of weight sets, this may require an excessively large
number of executions of such an algorithm, thus incurring a prohibitively large
running time.
  We indicate that, quite often, the different edge weights reflect different
combinations of some "raw" performance metrics (e.g., delay, cost). In such
cases, there is an inherent dependency among the different weights of the same
edge. This may well result in some similarity among the shortest routes, each
of which being optimal with respect to a specific set of weights. In this
study, we aim to exploit such similarity in order to improve the performance of
the solution scheme.
  Specifically, we contemplate edge weights that are obtained through different
linear combinations of some (``raw'') edge performance metrics. We establish
and validate a novel algorithm that efficiently computes a shortest path for
each set of edge weights. We demonstrate that, under reasonable assumptions,
the algorithm significantly outperforms the standard approach. Similarly to the
standard approach, the algorithm iteratively searches for routes, one per set
of edge weights; however, instead of executing each iteration independently, it
reduces the average running time by skillfully sharing information among the
iterations.
