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Examples of a Pareto Front
Left:
there
is
a strong trade-off
between the objectives/ objective functions
f
1
and
f
2
.
The smaller
the
f
1
value is that we want the larger is the corresponding
f
2
value
.
The
“ideal point/plan” I
lies far
away form the front.
There is a high dependence on the selection of the
f
1
value
.
I
Right:
there
is
a weak trade-off
between the objectives/ objective functions
f
1
and
f
2
.
It is possible
to optimise (minimise) the
f
1
significant and close to the
“ideal point/plan” I.
Only very close to
I
we observe a rapid increase of
f
2
.
This is a case where for a set of parameters
we can obtain
simultaneously almost individual optimal values for
f
1
and
f
2
I
The
“ideal solution/plan” I:
I = (f
1,min
, f
2,min
)
Inverse Optimisation and Planning: A Multi-Objective (MO) Problem
Strong trade-off
Weak trade-off