  A linear connection on a Finsler manifold is called compatible to the metric
if its parallel transports preserve the Finslerian length of tangent vectors.
Generalized Berwald manifolds are Finsler manifolds equipped with a compatible
linear connection. Since the compatibility to the Finslerian metric does not
imply the unicity of the linear connection in general, the first step of
checking the existence of compatible linear connections on a Finsler manifold
is to choose the best one to look for. A reasonable choice is introduced in
\cite{V14} called the extremal compatible linear connection, which has torsion
of minimal norm at each point.
  Randers metrics are special Finsler metrics that can be written as the sum of
a Riemannian metric and a 1-form (they are "translates" of Riemannian metrics).
In this paper, we investigate the compatibility equations for a linear
connection to a Randers metric. Since a compatible linear connection is
uniquely determined by its torsion, we transform the compatibility equations by
taking the torsion components as variables. We determine when these equations
have solutions, i.e. when the Randers space becomes a generalized Berwald space
admitting a compatible linear connection. Describing all of them, we can select
the extremal connection with the norm minimizing property. As a consequence, we
obtain the characterization theorem in \cite{Vin1}: a Randers space is a
non-Riemannian generalized Berwald space if and only if the norm of the
perturbating term with respect to the Riemannian part of the metric is a
positive constant.
