Because a physical process governing equations for upper scale heterogeneous medium are different from homogeneous (often it is for the lower scale of the same process) medium governing equations, the Optimization problem which mostly needs to be formulated for the Upper scale criteria should be differently formulated by definition from the homogeneous distributed parameters optimization tasks. The first work in this direction which specifically pointed out into connection between optimization purposes and the VAT controls in the governing equations was published in 1994 -
More on this area see in ..\Optimization_in_Heterogeneous_Media