Weighted multiobjective optimization problem

With weighting-faetor methods, the basie idea is to form a multiobjective optimization problem in whieh some faetor related to dynamie eontrollability is added to the traditional steady-state eeonomie faetors. These two faetors are suitably weighted, and the sum of the two is minimized (or maximized). The dynamic controllability factor can be some measure of the goodness of eontrol (integral of the squared error), the eost of the eontrol effort, or the value of some controllability measure (sueh as the plant eondition number, to be diseussed in Chapter 9). One real problem with these approaehes is the diffieulty of determining suitable weighting faetors. It is not elear how to do this in a general, easily applied way. 

Table 2. The crisp multiobjective optimization problem using the weighted sum method.

Here, the integrated design problem is formulated as a multiobjective optimization problem, where the objective functions to be minimized are a weighted sum of economic terms (Fi) and the Integral Square Error (ISE) ... 

In other words, the solution of problem [7.2] can be interpreted as a compromise solution relative to a utopia point given by the collection of the ideal stakeholder weighted costs wjf. This definition of utopia point is not to be confused with the traditional definition used in multiobjective optimization [6]. 

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