Environmental Engineering Reference
In-Depth Information
It may be that the original boundaries of the optimisation object were
chosen unsuccessfully. This becomes clear in further analysis of the system
and its mathematical model, interpretation of the search results of optimum
solutions, comparing them with practice, etc. Then, in some cases, the
system boundaries should be expanded while in others they should be made
narrower. To facilitate the search for optimum solutions it is reasonable to
explore each section as a separate selected system.
Generally, in engineering practice it is necessary, wherever possible, to
try to to simplify the system to be optimised, break up complex systems
into simpler subsystems, if it is believed that this will affect the final result
within acceptable limits.
Selection of controlled variables
At this stage of modelling it is important to distinguish between those
variables whose values can vary and be chosen with a view to achieving
the best results (controlled variables), and the values that are fixed or
determined by external factors. Determination of the values of controlled
variables which correspond to the best (optimum) situation is the task of
optimisation. Depending on the selected boundaries of the system to be
optimised and the level of accuracy of system description, the same values
can be either controlled variables or not.
Determination of restrictions on the controlled variables
In the real conditions, the choice of the controlled variables is usually
restricted due to the limits of available resources, facilities and other
features. When constructing a mathematical model, these restrictions are
usually written in the form of equalities and inequalities or determine sets
to which the values of the controlled variables must belong. The set of all
restrictions on the controlled variables defines the so-called permissible
set of optimisation tasks.
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Selection of the numerical criterion of optimisation
The obligatory part of the mathematical model of the optimisation object
is a numerical criterion, with the optimum variant of behaviour of the
investigated object corresponding to the minimum or maximum value of this
criterion (depending on the task). This criterion is completely determined
by the selected values of controlled variables, i.e. it is a function of these
variables and is called the target function.
Combining the results of previous stages of constructing the mathematical
statistical model, the model is written in the form of a mathematical
optimisation problem which includes building a target function and the
defined constraints on the controlled variables. In a sufficiently general form
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