  This paper introduces a novel framework for model adaptivity in the context
of heterogeneous multiscale problems. The framework is based on the idea to
interpret model adaptivity as a minimization problem of local error indicators,
that are derived in the general context of the Dual Weighted Residual (DWR)
method. Based on the optimization approach a post-processing strategy is
formulated that lifts the requirement of strict a priori knowledge about
applicability and quality of effective models. This allows for the systematic,
"goal-oriented" tuning of effective models with respect to a quantity of
interest.
  The framework is tested numerically on elliptic diffusion problems with
different types of heterogeneous, random coefficients, as well as an
advection-diffusion problem with strong microscopic, random advection field.
