The objective function provides an indicator of the quality of the correlation between File 1 and File 2 modes. It is a minimum objective function, which means that two perfectly well-correlated models yield an optimum value of 0. The objective function ƒ is computed as:
Where the following nomenclature is employed:
ƒ Objective Function.
𝛂 Weight of the frequency term.
frequency of the 
-th File 1 mode in the
diagonal of the MAC matrix.
frequency of the -th File 2 mode in the
diagonal of the MAC matrix.
-th value of the
diagonal of the MAC matrix.
If the automatic mode pairing algorithm is set, the modes in the diagonal of the MAC matrix are the paired modes. If it is not set, the modes that happen to be in the diagonal of the MAC matrix are the ones employed in the expression.
Therefore, if an optimization/design point analysis is to be conducted, Ansys recommends that the Pair Modes Property of the MAC Calculator Details view is set to . This will trigger the automatic mode pairing algorithm before the objective function is computed.