When analyzing systems with a large number of parameters, the dimen
sion of the original system may present insurmountable difficulties
for the analysis. It may then be convenient to reformulate the
original system in terms of substantially fewer aggregated
variables, or macrovariables. In other words, an original system
with an n-dimensional vector of states is reformulated as a system
with a vector of dimension much less than n. The aggregated
variables are either readily defined and processed, or the
aggregated system may be considered as an approximate model for the
orig inal system. In the latter case, the operation of the original
system can be exhaustively analyzed within the framework of the
aggregated model, and one faces the problems of defining the rules
for introducing macrovariables, specifying loss of information and
accuracy, recovering original variables from aggregates, etc. We
consider also in detail the so-called iterative aggregation
approach. It constructs an iterative process, at. every step of
which a macroproblem is solved that is simpler than the original
problem because of its lower dimension. Aggregation weights are
then updated, and the procedure passes to the next step.
Macrovariables are commonly used in coordinating problems of
hierarchical optimization."
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