
91Decision Analysis with Multiple Attributes
butes, a solution
P
belongs on the Pareto front if there is no other solution
P
, such that
≤∀∈∃
xx
1,.., and1,.., such that
* *
yy injn
i
P
i
P
j
P
j
P
(3 . 31)
A Pareto front can be dened on as many attributes as one desires; how-
ever, nding a Pareto front over many attributes and visually depicting it
becomes a challenge. Except for some simple problems, generating a Pareto
front is accomplished using multiobjective optimizers designed for that pur-
pose. There are mainly two ways to do this: optimizing convex combination
of attributes and nondominated sorting.
1. Optimizing convex ...