In mathematical form, multi-objective can be defined as
where, 
is a vector type objectives and the
functional 
is called as
a preference function. The preference function is an equivalent functional that
transform the vector type objective into a scalar type objective. In order to
represent our preference function, let’s consider following two objectives.
and
There are many preference functions in multi-objective optimization strategy. Among them, RecurDyn/AutoDesign uses following two types.
where, the values of 
are the user defined weighting
coefficients and the relaxation factors 
and 
are automatically determined. Also,
the ideal solution 
is
internally determined.