  We extend the notion of an enumeration scheme developed by Zeilberger and
Vatter to the case of vincular patterns (also called "generalized patterns" or
"dashed patterns"). In particular we provide an algorithm which takes in as
input a set $B$ of vincular patterns and search parameters and returns a
recurrence (called a "scheme") to compute the number of permutations of length
$n$ avoiding $B$ or confirmation that no such scheme exists within the search
parameters. We also prove that if $B$ contains only consecutive patterns and
patterns of the form $\sigma_1\sigma_2 ... \sigma_{t-1}-\sigma_t$, then such a
scheme must exist and provide the relevant search parameters. The algorithms
are implemented in Maple and we provide empirical data on the number of small
pattern sets admitting schemes. We make several conjectures on
Wilf-classification based on this data. We also outline how to refine schemes
to compute the number of $B$-avoiding permutations of length $n$ with $k$
inversions.
